Holographic c-theorems

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Counterexample to a-theorem: (Shapere & Tachikawa, 0809.3238) • flow between two N = 2 superconformal gauge theories UV: gauge group SU(N c +1) with N f =2N c fundamental hyper’s IR: gauge group SU(N c ) with N f =2N c fundamental hyper’s (m=0) ( ) • loophole: accidental U(1) symmetry appears in the IR limit • Possibilities: i) no theorem exists Today’s Talk ii) “C-theorem” exists but C(g*) ≠ a iii) “C-theorem” exists and C(g*) = a, but theorem needs fine-print for d>2 iv) something more interesting universal not universal
C-<strong>theorems</strong> in higher dimensions d=2: d=4: and • in 4 dimensions, have three central charges: • do any of these obey a similar “c-theorem” under RG flows -theorem: proposed by Cardy (1988) • numerous nontrivial examples, eg, perturbative fixed points (Jack & Osborn), SUSY gauge theories (Anselmi et al) • holographic field theories with gravity dual • no completely general proof • counterexample proposed: Shapere & Tachikawa, 0809.3238
Page 2 and 3: Motivation: “role of higher curva
Page 4 and 5: C-theorems in higher dimensions d=2
Page 6 and 7: SUSY example: (Anselmi, Freedman, G
Page 8 and 9: C-theorems in higher dimensions d=2
Page 14 and 15: Holographic RG flows: • for gener
Page 16 and 17: Holographic RG flows: (Freedman, Gu
Page 18 and 19: Improved Holographic RG Flows: •
Page 20 and 21: Improved Holographic RG Flows: •
Page 22 and 23: Higher Curvature Terms without Deri
Page 24 and 25: Quasi-Topological gravity: (Myers,
Page 26 and 27: Quasi-Topological gravity: (Myers &
Page 28 and 29: RG flows in Quasi-Topological gravi
Page 32 and 33: Higher Dimensions: • straightforw
Page 34 and 35: What is where AdS curvature: • t
Page 38 and 39: More Improved Holographic RG Flows:
Page 48 and 49: and Entanglement Entropy • in 100
Page 50 and 51: and Entanglement Entropy • place
Page 52 and 53: and Entanglement Entropy (see Kulax
Page 54 and 55: and Entanglement Entropy • we had
Page 56 and 57: and Entanglement Entropy • consid
Page 58 and 59: and Entanglement Entropy • puzzle
Page 60 and 61:
entanglement entropy: for even d fo
Page 62 and 63:
and Beyond: • Susskind & Witten:
Page 64 and 65:
and Beyond: • Susskind & Witten:
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Holographic c-theorems

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