String Theory and M-Theory

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Homework Problems 147 PROBLEM 4.14 Consider the ghost contributions to the super-Virasoro generators in the NS sector. (i) Work out the mode expansions for ghost contributions to Ln <strong>and</strong> Gr implied by Eqs (4.142) <strong>and</strong> (4.143). (ii) Prove that these generate a super-Virasoro algebra with ĉ = −10. PROBLEM 4.15 Using the method sketched in the text, show that the BRST charge in Eq. (4.150) is nilpotent for the critical dimension D = 10.
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This is the first comprehensive tex
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cambridge university press Cambridg
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vi An Ode to the Unity of Time and
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viii Contents 4.5 Canonical quantiz
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Preface String theory is one of the
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Preface xiii stein of Caltech for t
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Preface xv NL, NR left- and right-m
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1 Introduction There were two major
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1.2 General features 3 theory fell
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1.2 General features 5 is only cons
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1.3 Basic string theory 7 world she
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1.4 Modern developments in superstr
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2 The bosonic string This chapter i
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2.1 p-brane actions 19 choice of pa
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particle, namely 2.1 p-brane action
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SOLUTION 2.1 p-brane actions 23 The
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where ˙X µ = ∂Xµ ∂τ 2.2 The
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Tαβ, that is, 2.2 The string acti
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2.2 The string action 29 where we h
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2.3 String sigma-model action: the
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2.4 Canonical quantization 37 compo
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2.4 Canonical quantization 39 These
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finds that Eq. (2.85) is solved by
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where N = 2.4 Canonical quantizatio
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In fact, any such state can be reca
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2.4 Canonical quantization 47 Criti
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2.5 Light-cone gauge quantization 4
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2.5 Light-cone gauge quantization 5
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Homework Problems 53 The closed str
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(i) Dirichlet boundary conditions a
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Homework Problems 57 PROBLEM 2.11 T
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3.1 Conformal field theory 59 and r
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3.1 Conformal field theory 61 rotat
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symmetry, this tensor is also conse
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3.1 Conformal field theory 65 This
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3.1 Conformal field theory 67 Such
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or the equivalent commutation relat
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3.1 Conformal field theory 71 An im
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3.1 Conformal field theory 73 is pr
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SOLUTION 3.2 BRST quantization 75 A
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where TX is given in Eq. (3.23) and
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3.2 BRST quantization 79 in differe
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SOLUTION 3.3 Background fields 81 U
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3.3 Background fields 83 unoriented
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3.4 Vertex operators 85 3.4 Vertex
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3.4 Vertex operators 87 must act on
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3.5 The structure of string perturb
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SOLUTION 3.5 The structure of strin
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3.6 The linear-dilaton vacuum and n
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3.7 Witten’s open-string field th
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form Homework Problems 107 Φ(z) =
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4 Strings with world-sheet supersym
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4.1 Ramond-Neveu-Schwarz strings 11
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4.2 Global world-sheet supersymmetr
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4.3 Constraint equations and confor
Page 276: EXERCISES 4.3 Constraint equations
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Page 284: 4.5 Canonical quantization of the R
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Page 316: 4.7 SCFT and BRST 141 which now has
Page 320: 4.7 SCFT and BRST 143 These contrib
Page 324: Homework Problems 145 needs to incl
Page 330: 5 Strings with space-time supersymm
Page 334: 150 Strings with space-time supersy
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172 Strings with space-time supersy
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188 T-duality and D-branes physical
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190 T-duality and D-branes where
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192 T-duality and D-branes Vα =
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194 T-duality and D-branes directio
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196 T-duality and D-branes Chan-Pat
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198 T-duality and D-branes mitian m
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200 T-duality and D-branes If two
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202 T-duality and D-branes X µ R =
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204 T-duality and D-branes space va
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206 T-duality and D-branes one-form
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208 T-duality and D-branes to a D3-
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210 T-duality and D-branes and Diri
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212 T-duality and D-branes where A
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214 T-duality and D-branes account
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216 T-duality and D-branes µp Ap+
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218 T-duality and D-branes EXERCISE
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220 T-duality and D-branes directio
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222 T-duality and D-branes Anomalie
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224 T-duality and D-branes the hete
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226 T-duality and D-branes gauge sy
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228 T-duality and D-branes D-branes
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230 T-duality and D-branes spinors,
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232 T-duality and D-branes By T-dua
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234 T-duality and D-branes One reas
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236 T-duality and D-branes and in t
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238 T-duality and D-branes the Cher
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240 T-duality and D-branes which ar
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242 T-duality and D-branes matrix,
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244 T-duality and D-branes What typ
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246 T-duality and D-branes PROBLEM
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248 T-duality and D-branes PROBLEM
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250 The heterotic string string the
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252 The heterotic string 7.2 Fermio
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254 The heterotic string where µ =
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256 The heterotic string Left-mover
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258 The heterotic string which is a
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260 The heterotic string it is natu
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262 The heterotic string even, and
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264 The heterotic string where λ A
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266 The heterotic string The bosoni
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268 The heterotic string KI, which
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270 The heterotic string following.
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272 The heterotic string • The Fo
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274 The heterotic string In the cas
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276 The heterotic string Modular in
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278 The heterotic string The metric
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280 The heterotic string the circle
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282 The heterotic string as require
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284 The heterotic string contributi
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286 The heterotic string symmetry.
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288 The heterotic string Duality an
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290 The heterotic string (ii) (iii)
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292 The heterotic string SO(32) cur
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294 The heterotic string whose inne
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8 M-theory and string duality Durin
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298 M-theory and string duality bel
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300 M-theory and string duality cha
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302 M-theory and string duality Ele
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304 M-theory and string duality are
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306 M-theory and string duality The
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308 M-theory and string duality in
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310 M-theory and string duality tra
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312 M-theory and string duality Eq.
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314 M-theory and string duality The
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316 M-theory and string duality tra
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318 M-theory and string duality Res
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320 M-theory and string duality giv
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322 M-theory and string duality SOL
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324 M-theory and string duality sup
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326 M-theory and string duality wha
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328 M-theory and string duality are
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330 M-theory and string duality dua
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332 M-theory and string duality M-b
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334 M-theory and string duality Sin
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336 M-theory and string duality ten
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338 M-theory and string duality het
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340 M-theory and string duality and
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342 M-theory and string duality Thu
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344 M-theory and string duality dim
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346 M-theory and string duality cas
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348 M-theory and string duality Wha
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350 M-theory and string duality ten
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352 M-theory and string duality PRO
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9 String geometry Since critical su
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356 String geometry At sufficiently
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358 String geometry Fig. 9.1. This
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360 String geometry Noncompact exam
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362 String geometry In the quantum
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364 String geometry of the manifold
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366 String geometry 9.3 Examples of
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368 String geometry Hodge numbers o
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370 String geometry is a compact K
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372 String geometry proportional to
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374 String geometry This leads to t
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376 String geometry independent cho
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378 String geometry This implies th
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380 String geometry Kähler form an
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382 String geometry satisfies √ g
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384 String geometry In writing this
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386 String geometry This section an
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388 String geometry torus is descri
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390 String geometry where Mr is any
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392 String geometry Writing the met
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394 String geometry Since the prepo
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396 String geometry A change in the
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398 String geometry For these choic
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400 String geometry coefficients. W
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402 String geometry four fermionic
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404 String geometry a vanishing cyc
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406 String geometry global supersym
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408 String geometry similar fashion
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410 String geometry where K = 1 2 (
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412 String geometry versa. An early
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414 String geometry by complex-stru
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416 String geometry holonomy group,
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418 String geometry rather than SU(
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420 String geometry to the case of
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422 String geometry For example, in
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424 String geometry example is the
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426 String geometry type IIA string
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428 String geometry which transform
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430 String geometry The tension of
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432 String geometry fibration. Only
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434 String geometry folds, constrai
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436 String geometry to that in Exer
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438 String geometry be interpreted
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440 String geometry SOLUTION An inf
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442 String geometry to a zero form
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444 String geometry Riemannian geom
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446 String geometry map tensors to
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448 String geometry a possible holo
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450 String geometry as the complex
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452 String geometry . ✷ EXERCISE
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454 String geometry PROBLEM 9.8 Use
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10 Flux compactifications Moduli-sp
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458 Flux compactifications This hap
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460 Flux compactifications the stan
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462 Flux compactifications coordina
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464 Flux compactifications Fig. 10.
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466 Flux compactifications The last
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468 Flux compactifications forms (a
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470 Flux compactifications G µν G
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474 Flux compactifications Superpot
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476 Flux compactifications where dz
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478 Flux compactifications Since m
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480 Flux compactifications 10.2 Flu
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482 Flux compactifications is the e
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484 Flux compactifications the fibe
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486 Flux compactifications The tota
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488 Flux compactifications S 3 S 2
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490 Flux compactifications be true
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492 Flux compactifications where gs
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496 Flux compactifications Negative
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498 Flux compactifications will be
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500 Flux compactifications As you a
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502 Flux compactifications where K
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504 Flux compactifications is of in
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506 Flux compactifications V(σ) Fi
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508 Flux compactifications where Da
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512 Flux compactifications M, N, P
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514 Flux compactifications By defin
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516 Flux compactifications In this
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518 Flux compactifications As a res
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520 Flux compactifications constant
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522 Flux compactifications a way th
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524 Flux compactifications F3 −
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526 Flux compactifications One fina
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528 Flux compactifications Friedman
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530 Flux compactifications If there
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532 Flux compactifications cosmolog
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534 Flux compactifications to Eq. (
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536 Flux compactifications but not
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538 Flux compactifications e-foldin
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540 Flux compactifications of makin
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542 Flux compactifications Here W0
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544 Flux compactifications [γmn,
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546 Flux compactifications complex
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548 Flux compactifications Eq. (10.
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550 Black holes in string theory th
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552 Black holes in string theory di
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554 Black holes in string theory He
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556 Black holes in string theory r=
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558 Black holes in string theory
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560 Black holes in string theory of
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562 Black holes in string theory Th
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564 Black holes in string theory wh
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566 Black holes in string theory SO
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570 Black holes in string theory st
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572 Black holes in string theory M-
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574 Black holes in string theory ro
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576 Black holes in string theory In
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578 Black holes in string theory Fi
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580 Black holes in string theory (2
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582 Black holes in string theory SO
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584 Black holes in string theory ju
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586 Black holes in string theory No
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588 Black holes in string theory co
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590 Black holes in string theory ba
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594 Black holes in string theory Fi
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596 Black holes in string theory su
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600 Black holes in string theory 28
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602 Black holes in string theory is
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606 Black holes in string theory S-
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608 Black holes in string theory PR
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12 Gauge theory/string theory duali
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612 Gauge theory/string theory dual
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Bibliographic discussion In the fol
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692 Bibliographic discussion The BR
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694 Bibliographic discussion derive
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696 Bibliographic discussion which
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698 Bibliographic discussion Maldac
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Bibliography Abouelsaood, A., Calla
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702 Bibliography Singapore: World S
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704 Bibliography Brink, L., and Nie
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706 Bibliography E-print hep-th/000
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708 Bibliography hep-th/0105203. Eg
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710 Bibliography Phys., 71, 983-108
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712 Bibliography hep-th/9802109. Gu
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714 Bibliography Johnson, C. V. (20
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716 Bibliography Lerche, W., Schell
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718 Bibliography Montonen, C. (1974
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720 Bibliography Polchinski, J., an
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722 Bibliography Sen, A. (1999). No
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724 Bibliography Tseytlin, A. A. (1
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acceleration equation, 528 action p
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728 Index Calabi-Yau four-fold, 458
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730 Index with E6,6 symmetry, 570 c
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732 Index Friedmann equation, 528 F
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734 Index dual Coxeter number, 69 e
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736 Index homogeneity equation, 603
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738 Index superconformal symmetry,
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String Theory and M-Theory

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