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Bicudo, Pedro; Pisarski, Robert D.; Seel, Elina

doi:10.1103/physrevd.88.034007

Cited by 9 publications

(11 citation statements)

References 54 publications

(60 reference statements)

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“…Namely, we can replace the parameter c 3 in (8) with c 3 (∞) + (c 3 (1) − c 3 (∞))/t 2 where the variable t is equal to T /T c by definition. The improved models 3 are in good agreement with the lattice data and have been used in other studies [21,22,23,24,25,26].…”

Section: Review Of the Matrix Modelssupporting

confidence: 73%

“…The proof of (2) can be achieved by the following two steps. Firstly, by using the corresponding commutation relations of the group generators, we are able to get some simplified expressions for the two-loop effective potential which contain only the Bernoulli polynomials while the structure constants appear in (22) and (23) have been get rid of. Secondly, based on a set of relations of the Bernoulli polynomials, the simplified two-loop results are expressed in terms of B 4 (x).…”

Section: Two-loop Perturbation Corrections To the Effective Potentialmentioning

confidence: 99%

“…Firstly, we consider (22) in the case where only one of the indices a, b and c is the diagonal index 11 . By using the property of the roots α ij = 1 √ 2 ( e i − e j ) with an orthonormal basis { e i } spanning an N -dimensional space, we can get rid of the structure constants and write this kind of contribution as…”

Section: Proof For Su(n)mentioning

confidence: 99%

“…(2) f | II is the part with all the indices being off-diagonal in (22). To get these two equations, we have used (59) and (61) to get rid of the structure constants.…”

Section: Proof For So(2n) and So(2n + 1)mentioning

confidence: 99%

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Matrix models for deconfinement and their perturbative corrections

Yun

2014

J. High Energ. Phys.

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Matrix models for the deconfining phase transition in SU(N ) gauge theories have been developed in recent years. With a few parameters, these models are able to reproduce the lattice results of the thermodynamic quantities in the semi-quark gluon plasma(QGP) region. They are also used to compute the behavior of the 't Hooft loop and study the exceptional group G(2). In this paper, we review the basic ideas of the construction of these models and propose a new form of the non-ideal corrections in the matrix model. In the semi-QGP region, our new model is in good agreement with the lattice simulations as the previous ones, while in higher temperature region, it reproduces the upward trend of the rescaled trace anomaly as found in lattice which, however, can not be obtained from the previous models. In addition, we discuss the perturbative corrections to the thermal effective potential which could be used to systematically improve the matrix models at high temperatures. In particular, we provide, for the first time, an analytical proof of the relation between the one-and two-loop effective potential: two-loop correction is proportional to the one-loop result, independent of the eigenvalues of the Polyakov loop. This is a very general result, we prove it for all classic groups, including SU(N ), SO(2N +1), SO(2N ) and Sp(2N ).

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Section: Review Of the Matrix Modelssupporting

confidence: 73%

Section: Two-loop Perturbation Corrections To the Effective Potentialmentioning

confidence: 99%

Section: Proof For Su(n)mentioning

confidence: 99%

“…(2) f | II is the part with all the indices being off-diagonal in (22). To get these two equations, we have used (59) and (61) to get rid of the structure constants.…”

Section: Proof For So(2n) and So(2n + 1)mentioning

confidence: 99%

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Matrix models for deconfinement and their perturbative corrections

Yun

2014

J. High Energ. Phys.

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“…where c 1 is an unknown function of T . Model studies of the deconfining transition in 3 + 1 [22,26] and 2 + 1 dimensions [28] show that the pressure, or equivalently the interaction measure, depends sensitively on c 1 .…”

Section: Near the Gww Pointmentioning

confidence: 99%

Finite-temperature phase transitions of third and higher order in gauge theories at large N

2018

Self Cite

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We study phase transitions in SUð∞Þ gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia. Depending upon the detailed form of the matrix model, the eigenvalue density and the behavior of the specific heat near the transition differ drastically. We speculate that in the pure gauge theory, although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infinite N.

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Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

Caselle,

Magnoli,

Nada

et al. 2024

J. High Energ. Phys.

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We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

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Matrix model for deconfinement in aSU(2)gauge theory in2+1dimensions

Cited by 9 publications

References 54 publications

Matrix models for deconfinement and their perturbative corrections

Matrix models for deconfinement and their perturbative corrections

Finite-temperature phase transitions of third and higher order in gauge theories at large N

Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

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