Topology, symmetry, and phase transitions in lattice gauge ... - tuprints

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A B S T R A C T We study connections between global symmetries, topological objects, and phase transitions in non-abelian gauge theories. The characterization of deconfinement as a spontaneous symmetry breaking transition in SU(N) gauge theories with static quarks, and its description in terms of Z N interfaces, serve as our motivation. We study 2 + 1 dimensional SU(N) gauge theories with N ≤ 4, which are candidates for the exploitation of universality with corresponding N-state Potts models. Exact results from the 2d spin systems are used to obtain critical couplings, transition temperatures, exponents, and the behavior of string tensions at criticality. Kramers- Wannier duality emerges between center vortices and electric fluxes at the phase transition for N ≤ 3, which is inherited from a finite volume self-duality of the 2d N-state Potts models. The form of the duality as a discrete Fourier transform over ensembles with interfaces emphasizes the link between confinement and topology in pure SU(N) gauge theories. We then investigate monopole inducing boundary conditions in SU(N) grand unified theories with an adjoint Higgs field, and find that non-trivial magnetic charge may be enforced but with several restrictions. Finally, we introduce dynamical quarks and the curious connection between confinement and their fractional electric charge. Owing to a coincidence of quantum numbers in the matter sector, the Standard Model possesses a hidden global center symmetry that is lost when Quantum Chromodynamics (QCD) is treated as an isolated theory. We discuss the topological implications of this symmetry, and investigate their influence on the phase structure of a 2-color lattice model with quarks that carry also a fractional electric charge. v
Page 1 and 2: T O P O L O G Y, S Y M M E T RY, A
Page 3: To Angela.
Page 7 and 8: C O N T E N T S 1 introduction 1 2
Page 9 and 10: I N T R O D U C T I O N 1 The marri
Page 11: introduction 3 Unification has a lo
Page 14 and 15: 6 gauge theories Invariance of the
Page 16 and 17: 8 gauge theories Unfortunately, gau
Page 18 and 19: 10 gauge theories Lattice actions t
Page 20 and 21: 12 gauge theories Figure 2.2: Paral
Page 23 and 24: U N I V E R S A L A S P E C T S O F
Page 25 and 26: universal aspects of confinement in
Page 27 and 28: 3.1 confinement of color flux 19 a
Page 29 and 30: 3.2 twisted ensembles 21 Figure 3.4
Page 31 and 32: 3.2 twisted ensembles 23 When cente
Page 33 and 34: 3.2 twisted ensembles 25 functions.
Page 35 and 36: 3.3 universality 27 These dualities
Page 37 and 38: 3.4 exploiting universality 29 wher
Page 39 and 40: 3.4 exploiting universality 31 1.04
Page 41 and 42: 3.4 exploiting universality 33 In t
Page 43 and 44: 3.4 exploiting universality 35 with
Page 45 and 46: 3.5 finite size scaling and self-du
Page 51 and 52: 3.6 exploiting self-duality 43 to l
Page 53 and 54: 3.6 exploiting self-duality 45 wher
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3.6 exploiting self-duality 47 with
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3.6 exploiting self-duality 49 ξ
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3.6 exploiting self-duality 51 N t
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3.7 su(3) in 2 + 1 d 53 Figure 3.20
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3.8 su(4) in 2 + 1 d 55 3.8 su(4) i
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3.8 su(4) in 2 + 1 d 57 14 12 10 32
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3.8 su(4) in 2 + 1 d 59 0 1 2 3 4 0
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3.8 su(4) in 2 + 1 d 61 8.5 8 8 3 1
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3.8 su(4) in 2 + 1 d 63 which is in
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66 ’t hooft monopoles in lattice
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F R A C T I O N A L E L E C T R I C
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5.1 center symmetry breaking by qua
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5.2 a hidden global symmetry 91 Fig
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5.2 a hidden global symmetry 93 The
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5.2 a hidden global symmetry 95 the
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5.2 a hidden global symmetry 97 Fig
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5.3 explorations in a 2-color world
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5.4 fundamental higgs with fraction
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5.5 discussion 115 5.5 discussion L
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5.5 discussion 117 ? Figure 5.16: (
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120 concluding remarks QCD-like the
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122 twist away from criticality A e
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124 twist away from criticality Fig
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126 twist away from criticality 1 a
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M O R E O N C - P E R I O D I C B O
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B.2 mixed c-periodic boundary condi
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138 low-energy representations from
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140 bibliography [15] L. von Smekal
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142 bibliography [46] H. J. Rothe,
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144 bibliography [74] P. Ginsparg,
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146 bibliography [104] G. ’t Hoof
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148 bibliography [135] C. Q. Geng,
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150 bibliography [165] M. Creutz, L
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A C K N O W L E D G M E N T S First
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