Phase structure of U(N→∞) gauge theory on a two-dimensional lattice for a broad class of variant actions

Jurkiewicz, J.; Zalewski, K.

doi:10.1016/0550-3213(83)90221-3

Cited by 65 publications

(90 citation statements)

References 11 publications

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“…Moreover, we may be able to examine how the phase structure in the zero 't Hooft coupling limit continues to the one in the large 't Hooft coupling limit. 27 For example, the Casimir energy on the trivial vacuum with the anti-periodic boundary condition (3.17) is about 4/3 times the mass of the Eguchi-Hanson soliton (4.12), thus one may wonder what would happen if we include λ correction. In the high temperature phase, we have observed that the relevant geometry is the orbifold of the AdS-Schwarzschild black hole, which is dual to the Z k symmetric vacuum.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…27 It might be useful to make use of the Penrose limit [41] to examine the intermediate regime. See [50,51] for the comparison of the Hagedorn temperature.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The general solutions subject to the normalization condition ρ I 0 = 1 can be obtained by following [27,3] in principle. However, the analysis is quite complicated generically, so we adopt an approximation by setting z I,J n (x) = 0 for n > 1.…”

Section: Just Above the Critical Temperaturesmentioning

confidence: 99%

“…Then the solution can be easily found as This is valid for x satisfying J z 0,J 1 (x) ≥ 1, and the equality holds for the critical temperature x = x c . The free energy is 27) and near the critical temperature Let us compare the free energies for the above two cases. For the case with the periodic boundary condition, the free energy for the Z k symmetric case is lower near the critical temperature, since the critical temperature is smaller in this case.…”

Section: Just Above the Critical Temperaturesmentioning

confidence: 99%

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Phase transitions of largeNorbifold gauge theories

Hikida¹

2006

J. High Energy Phys.

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We study the phase structures of N = 4 U (N ) super Yang-Mills theories on R × S 3 /Z k with large N . The theory has many vacua labelled by the holonomy matrix along the non-trivial cycle on S 3 /Z k , and for the fermions the periodic and the anti-periodic boundary conditions can be assigned along the cycle. We compute the partition functions of the orbifold theories and observe that phase transitions occur even in the zero 't Hooft coupling limit. With the periodic boundary condition, the vacua of the gauge theory are dual to various arrangements of k NS5-branes. With the anti-periodic boundary condition, transitions between the vacua are dual to localized tachyon condensations. In particular, the mass of a deformed geometry is compared with the Casimir energy for the dual vacuum. We also obtain an index for the supersymmetric orbifold theory. *

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…27 It might be useful to make use of the Penrose limit [41] to examine the intermediate regime. See [50,51] for the comparison of the Hagedorn temperature.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Just Above the Critical Temperaturesmentioning

confidence: 99%

Section: Just Above the Critical Temperaturesmentioning

confidence: 99%

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Phase transitions of largeNorbifold gauge theories

Hikida¹

2006

J. High Energy Phys.

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“…An effective theory is constructed directly by integrating out all modes with nonzero momentum, and gives a matrix model which is soluble at large N [13][14][15][16]. As a function of temperature, it exhibits a GrossWitten-Wadia transition [17].…”

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confidence: 99%

Gross-Witten-Wadia transition in a matrix model of deconfinement

Pisarski

Skokov

2012

Phys. Rev. D

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We study the deconfining phase transition at nonzero temperature in a SU (N ) gauge theory, using a matrix model which was analyzed previously at small N . We show that the model is soluble at infinite N , and exhibits a Gross-Witten-Wadia transition. In some ways, the deconfining phase transition is of first order: at a temperature T d , the Polyakov loop jumps discontinuously from 0 to 1 2 , and there is a nonzero latent heat ∼ N 2 . In other ways, the transition is of second order: e.g., the specific heat diverges as C ∼ 1/(T − T d ) 3/5 when T → T + d . Other critical exponents satisfy the usual scaling relations of a second order phase transition. In the presence of a nonzero background field h for the Polyakov loop, there is a phase transition at the temperature T h where the value of the loop = The properties of the deconfining phase transition for a SU (N ) gauge theory at nonzero temperature are of fundamental interest. At small N , this transition can only be understood through numerical simulations on the lattice [1]. Large N can be studied through numerical simulations [2] and in reduced models [3]. In the pure glue theory, this transition can be modeled through an effective model, such as a matrix model [4][5][6][7][8][9][10].One limit in which the theory can be solved analytically is by putting it on a sphere of femto-scale dimensions [11,12]. An effective theory is constructed directly by integrating out all modes with nonzero momentum, and gives a matrix model which is soluble at large N [13][14][15][16]. As a function of temperature, it exhibits a GrossWitten-Wadia transition [17]. That is, it exhibits aspects of both first order and second order phase transitions; thus it can be termed "critical first order" [12]. Since the theory has finite spatial volume, however, there is only a true phase transition at infinite N . Thus on a femtosphere, the Gross-Witten-Wadia transition appears to be mere curiosity.Matrix models have been developed as an effective theory for deconfinement in four spacetime dimensions (and infinite volume). These models, which involve zero [6], one [7], and two parameters [8,9], are soluble analytically for two and three colors, and numerically for four or more colors. In this paper we show that these models are also soluble analytically for infinite N . Most unexpectedly, we find that the model exhibits a Gross-Witten-Wadia transition, very similar to that on a femtosphere. This is surprising because on a femtosphere, the matrix model is dominated by the Vandermonde determinant, and looks nothing like the matrix models of Refs. [6][7][8][9]. This suggests that the Gross-Witten-Wadia transition may not be * pisarski@bnl.gov † vskokov@quark.phy.bnl.gov an artifact of a femtosphere, but might occur for SU (∞) gauge theories in infinite volume. At the end of this paper we estimate how large N must be to see signs of the Gross-Witten-Wadia transition at infinite N . I. ZERO BACKGROUND FIELDWe expand about a constant background field for the vector potential,where i, j = 1 . . ....

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Some New/Old Approaches to QCD

Gross

1993

Integrable Quantum Field Theories

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Phase structure of U(N→∞) gauge theory on a two-dimensional lattice for a broad class of variant actions

Cited by 65 publications

References 11 publications

Phase transitions of largeNorbifold gauge theories

Phase transitions of largeNorbifold gauge theories

Gross-Witten-Wadia transition in a matrix model of deconfinement

Some New/Old Approaches to QCD

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