A survey of large N continuum phase transitions

Narayanan, Rajamani; Neuberger, Herbert

doi:10.22323/1.042.0020

Cited by 10 publications

(24 citation statements)

References 53 publications

(77 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we consider higher order corrections of u 0 and u in the metric (17) as in [14], the corrected entropy depends on the temperature. the classical action (18) we can see that the Z N symmetry along the x 4 -cycle is also broken. Thus the Polyakov loop W 0 and W 4 in this solution are both nonzero as shown in Table 1 and, contrary to the black D4 solution, the localized solitonic D3 solution is appropriate for a description of the deconfinement phase in the dual gauge theory (which also has W 0 = 0, W 4 = 0).…”

Section: Gregory-laflamme Transition In the Gravity Theory With (Papmentioning

confidence: 91%

“…Especially, if the Z N symmetry is preserved, physical quantities do not depend on the temporal radius β/2π at O(N 2 ) order due to 'large N volume independence' [15,16,17]. If the gauge theory is on a torus S 1 L 1 × S 1 L 2 × · · · , the large N volume independence is generalized and physical quantities do not depend on L i , if the Z N symmetry along the i-th direction is preserved [18].…”

Section: 1 Finite Temperature Qcdmentioning

confidence: 99%

“…(12.11) in [14] with p = 4 through identification L = β andT = 1/L 4 . 18 The GL instability was initially found in the black string. However similar instability exists in the solitonic solutions as well; the reason is easily understood in the Euclidian space, where there are no differences between the black objects and solitonic solutions.…”

Section: Gregory-laflamme Transition In the Gravity Theory With (Papmentioning

confidence: 99%

See 2 more Smart Citations

Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD

Mandal

Morita

2011

J. High Energ. Phys.

View full text Add to dashboard Cite

We discuss the phase structure of N D4 branes wrapped on a temporal (Euclidean) and a spatial circle, in terms of the near-horizon geometries. This system has been studied previously to understand four dimensional pure SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the subject, the phase transition between the solitonic D4 brane and the black D4 brane is interpreted as the strong coupling continuation of the confinement/deconfinement transition in YM4. We show that this interpretation is not valid, since the black D4 brane and the deconfinement phase of YM4 have different realizations of the Z N centre symmetry and cannot be identified. We propose an alternative gravity dual of the confinement/deconfinement transition in terms of a Gregory-Laflamme transition of the soliton in the IIB frame, where the strong coupling continuation of the deconfinement phase of YM4 is a localized D3 soliton. Our proposal offers a new explanation of several aspects of the thermodynamics of holographic QCD. As an example, we show a new mechanism of chiral symmetry restoration in the Sakai-Sugimoto model. The issues discussed in this paper pertain to gravity duals of non-supersymmetric gauge theories in general.

show abstract

Section: Gregory-laflamme Transition In the Gravity Theory With (Papmentioning

confidence: 91%

Section: 1 Finite Temperature Qcdmentioning

confidence: 99%

Section: Gregory-laflamme Transition In the Gravity Theory With (Papmentioning

confidence: 99%

See 1 more Smart Citation

Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD

Mandal

Morita

2011

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Another variant of the original model that originally seemed promising is the Twisted EK (TEK) model [205], but more recent extensive lattice simulations indicate center symmetry breaking in this model as well [206][207][208]. An interesting alternative to single-site reduction is to simulate large-N theories on lattices of size N 4 s , and keep N s sufficiently large that the deconfinement transition is avoided [184,209]. As long as center symmetry is maintained, such models will be equivalent to infinite-volume theories in the limit of infinite N .…”

Section: A Eguchi-kawai Modelsmentioning

confidence: 99%

Phases of gauge theories

Ogilvie¹

2012

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

One of the most fundamental questions we can ask about a given gauge theory is its phase diagram. In the standard model, we observe three fundamentally different types of behavior: QCD is in a confined phase at zero temperature, while the electroweak sector of the standard model combines Coulomb and Higgs phases. Our current understanding of the phase structure of gauge theories owes much to the modern theory of phase transitions and critical phenomena, but has developed into a subject of extensive study. After reviewing some fundamental concepts of phase transitions and finite-temperature gauge theories, we discuss some recent work that broadly extends our knowledge of the mechanisms that determine the phase structure of gauge theories. A new class of models with a rich phase structure has been discovered, generalizing our understanding of the confinement-deconfinement transition in finite-temperature gauge theories. Models in this class have space-time topologies with one or more compact directions. On R 3 ×S 1 , the addition of double-trace deformations or periodic adjoint fermions to a gauge theory can yield a confined phase in the region where the S 1 circumference L is small, so that the coupling constant is small, and semiclassical methods are applicable. In this region, Euclidean monopole solutions, which are constituents of finite-temperature instantons, play a crucial role in the calculation of a non-perturbative string tension. We review the techniques use to analyze this new class of models and the results obtained so far, as well as their application to finite-temperature phase structure, conformal phases of gauge theories and the large-N

show abstract

“…If the volume of Σ is finite, there is no sharp phase transition, but for an SU(N) gauge theory in the large N limit there are sharply demarcated phases depending on the shape and size parameters of Σ. In case the compact space is a torus, the phase diagram as a function of various radii (and coupling) reveals a rich phase structure [2,3], including a cascade of phase transitions in which the "Polyakov" loops along various non-contractible cycles become non-zero in succession as the radii are reduced [4,5]. Most of these studies are numerical (in the lattice or in the continuum) or, in some cases, based on holography (see Section 6 for references and more details).…”

Section: Introductionmentioning

confidence: 99%

Phases of a two-dimensional large-Ngauge theory on a torus

Mandal

Morita

2011

Phys. Rev. D

View full text Add to dashboard Cite

We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2 dimensional pure Yang-Mills theory on T D+2 with D small radii. The two dimensional model has various phases characterized by the holonomy of the gauge field around non-contractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method, developed in an earlier work (hepth/0910.4526), which is nonperturbative in the 'tHooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D + 2 dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations (hep-lat/0710.0098). We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation. N . The α(x µ ) are valid gauge transformations locally, and leave local colour-singlets e.g. trF 2 µν invariant; in particular they commute with the hamiltonian. However, under the α-transformations W µ → h µ W µ . A non-zero value of W µ implies spontaneous symmetry breaking of the centre symmetry in the µ-direction.4 Kaluza Klein reduction is tricky for gauge theories [3,11], since in the confined phase the KK modes can have energies ∼ 1/(N L), which become arbitrarily low at large N . The fractional modes, equivalent to the 'long string' modes of [12], can be understood as arising from mode shifts of charged fields in the presence of Wilson lines whose eigenvalues are uniformly distributed along a circle (see Section 2 for an explicit verification for this statement). In the deconfined phase, however, the KK modes have energies ∼ 1/L, like in ordinary field theories, and KK reduction proceeds as usual.

show abstract

A survey of large N continuum phase transitions

Cited by 10 publications

References 53 publications

Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD

Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD

Phases of gauge theories

Phases of a two-dimensional large-Ngauge theory on a torus

Contact Info

Product

Resources

About