Matrix Model Thermodynamics

Semenoff, Gordon W.

doi:10.1142/9789812702340_0071

Cited by 8 publications

(14 citation statements)

References 57 publications

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“…These models share the same symmetry SU(2|4) at zero temperature, and the gravity dual of these models was studied in [6]. The thermodynamics of plane wave matrix model has been studied in [42,43,44,45,46], and, in particular, the different vacua was compared in [46]. The thermodynamics of large N gauge theory on R × S 2 should be also interesting.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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%

Phase transitions of largeNorbifold gauge theories

Hikida¹

2006

J. High Energy Phys.

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“…[13,17] it was argued that the phase transition that we shall study here occurs only when there is a residual gauge symmetry and only in the limit where the rank of the residual gauge group goes to infinity. According to ref.…”

Section: Classical Ground Statesmentioning

confidence: 99%

“…The results of refs. [13,17] can be interpreted as saying that the phase transition of the matrix model occurs only in 5-brane states and not in membrane states, and it seems to be associated with internal dynamics of the 5-branes. Of course, refs.…”

Section: Classical Ground Statesmentioning

confidence: 99%

Free energy and phase transition of the matrix model on a plane wave

et al. 2005

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It has recently been observed that the weakly coupled plane wave matrix model has a density of states which grows exponentially at high energy. This implies that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. In this paper, we analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator in the finite temperature plane-wave matrix model to three loop order. We show that the phase transition is indeed of first order. We also compute the correction to the Hagedorn temperature to order two loops.

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“…Therefore, the eigenvalues for the higher spin 3 current in this higher representation in both linear and nonlinear versions are the same as each other 49 . 49 In the similar higher representation, one obtains (k + N + 2)…”

Section: The (F ; F) Representationmentioning

confidence: 97%

“…It is not obvious to see these basis at first sight. There is other way to obtain these basis by using the roots and weights [49]. After applying the 24 generators which are 5 × 5 matrices in (A.1) to (D.1), the 24 generators in terms of 40 × 40 unitary matrix are given as follows.…”

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confidence: 99%

Wolf space coset spectrum in the large ${{\mathcal N}}=4$ holography

Ahn

2018

J. Phys. A: Math. Theor.

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After reviewing the four eigenvalues (the conformal dimension, two SU(2) quantum number, and U(1) charge) in the minimal (and higher) representations in the Wolf space coset where the N = 4 superconformal algebra is realized by 11 currents in nonlinear way, these four eigenvalues in the higher representations up to three boxes (of Young tableaux) are examined in detail. The eigenvalues associated with the higher spin-1, 2, 3 currents in the (minimal and) higher representations up to two boxes are studied. They are expressed in terms of the two finite parameters (N, k) where the Wolf space coset contains the group SU(N + 2) and the affine Kac-Moody spin 1 current has the level k. Under the large (N, k) 't Hooft-like limit, they are simply linear combinations of the eigenvalues in the minimal representations. For the linear case where the N = 4 superconformal algebra is realized by 16 currents in linear way, the eigenvalues, corresponding to the spin 2 current and the higher spin 3 current, which are the only different quantities (compared to the nonlinear case), are also obtained at finite (N, k). They coincide with the results for the nonlinear case above after the large (N, k) 't Hooft-like limit is taken. As a by product, the three-point functions of the higher spin currents with two scalar operators can be determined at finite (N, k).

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Matrix Model Thermodynamics

Cited by 8 publications

References 57 publications

Phase transitions of largeNorbifold gauge theories

Phase transitions of largeNorbifold gauge theories

Free energy and phase transition of the matrix model on a plane wave

Wolf space coset spectrum in the large ${{\mathcal N}}=4$ holography

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