Exactly solvable unitary matrix models: Multicritical potentials and correlations

Periwal, Vipul; Shevitz, Danny

doi:10.1016/0550-3213(90)90676-5

Cited by 112 publications

(158 citation statements)

References 5 publications

Supporting

Mentioning

155

Contrasting

Order By: Relevance

“…• The above situation is identical with what was seen in the unitary one-matrix model of two-dimensional U(N ) lattice gauge theory [24,25] or of one-dimensional type 0 string theories [30]. The unitary matrix model has two phases in the planar limit, which correspond to weakly and strongly coupled regions of the gauge theory, respectively.…”

Section: Jhep09(2014)104supporting

confidence: 58%

“…1 Consequently we shall find that the full nonperturbative free energy is expressed in terms of a Painlevé II transcendent, in coincidence with the unitary one-matrix model [24,25]. It suggests correspondence between two-dimensional U(N ) gauge theory and some sector of the two-dimensional IIA superstring theory, as well as partial equivalence of the IIA superstrings to one-dimensional type 0 strings.…”

Section: Jhep09(2014)104mentioning

confidence: 99%

“…Transition between these phases is also of the third order [31,32]. A double scaling limit of the model (and its generalized versions) was investigated by using orthogonal polynomial methods in [24,25], where the second derivative of the free energy is given in terms of the Hastings-McLeod solution. The functional form of the free energy is essentially the same as our result except the leading planar contribution, which is smooth across the two phases, i.e.…”

Section: Jhep09(2014)104mentioning

confidence: 99%

See 2 more Smart Citations

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

Nishigaki

Sugino

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

We present an analytic expression of the nonperturbative free energy of a double-well supersymmetric matrix model in its double scaling limit, which corresponds to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. To this end we draw upon the wisdom of random matrix theory developed by Tracy and Widom, which expresses the largest eigenvalue distribution of unitary ensembles in terms of a Painlevé II transcendent. Regularity of the result at any value of the string coupling constant shows that the third-order phase transition between a supersymmetry-preserving phase and a supersymmetry-broken phase, previously found at the planar level, becomes a smooth crossover in the double scaling limit. Accordingly, the supersymmetry is always broken spontaneously as its order parameter stays nonzero for the whole region of the coupling constant. Coincidence of the result with the unitary one-matrix model suggests that one-dimensional type 0 string theories partially correspond to the type IIA superstring theory. Our formulation naturally allows for introduction of an instanton chemical potential, and reveals the presence of a novel phase transition, possibly interpreted as condensation of instantons.

show abstract

Section: Jhep09(2014)104supporting

confidence: 58%

Section: Jhep09(2014)104mentioning

confidence: 99%

Section: Jhep09(2014)104mentioning

confidence: 99%

See 1 more Smart Citation

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

Nishigaki

Sugino

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…See for example the bottom curves of the families depicted in figure 2(a) and (b). The cases of k = 1, 2 and 3 have been studied extensively, and (at least) k = 1 is known to exist uniquely (since it maps [44,45] to the case of the simplest Unitary matrix model critical point [46,47] which defines unique physics [48,49]) and this at least implies a unique family for all k connected by KdV flows [42].…”

Section: The String Equationsmentioning

confidence: 99%

Tachyon Condensation, Open-Closed Duality, Resolvents, and Minimal Bosonic and Type 0 Strings

Johnson

2005

J. High Energy Phys.

View full text Add to dashboard Cite

Type 0A string theory in the (2, 4k) superconformal minimal model backgrounds and the bosonic string in the (2, 2k − 1) conformal minimal models, while perturbatively identical in some regimes, may be distinguished non-perturbatively using double scaled matrix models. The resolvent of an associated Schrödinger operator plays three very important interconnected roles, which we explore perturbatively and non-perturbatively. On one hand, it acts as a source for placing D-branes and fluxes into the background, while on the other, it acts as a probe of the background, its first integral yielding the effective force on a scaled eigenvalue. We study this probe at disc, torus and annulus order in perturbation theory, in order to characterize the effects of D-branes and fluxes on the matrix eigenvalues. On a third hand, the integrated resolvent forms a representation of a twisted boson in an associated conformal field theory. The entire content of the closed string theory can be expressed in terms of Virasoro constraints on the partition function, which is realized as wavefunction in a coherent state of the boson. Remarkably, the D-brane or flux background is simply prepared by acting with a vertex operator of the twisted boson. This generates a number of sharp examples of open-closed duality, both old and new. We discuss whether the twisted boson conformal field theory can usefully be thought of as another holographic dual of the non-critical string theory.

show abstract

“…In fact, (55) is incredibly tantalising because in the vicinity of a Gross-Witten transition [10], the large N expansion does break down [34] and corrections need to be computed using a double scaling limit [35,36,37]. Near the transition point, corrections are given precisely in terms of N −2/3 !…”

Section: Solutions For Small κ ′mentioning

confidence: 99%

Multiply wound Polyakov loops at strong coupling

2006

View full text Add to dashboard Cite

We study the expectation value of a Polyakov-Maldacena loop that wraps the thermal circle k times in strongly coupled N = 4 super Yang-Mills theory. This is achieved by considering probe D3 and D5 brane embeddings in the dual black hole geometry. In contrast to multiply wound spatial Wilson loops, nontrivial dependence on k is captured through D5 branes. We find N −2/3 corrections, reminiscent of the scaling behaviour near a Gross-Witten transition.

show abstract

Exactly solvable unitary matrix models: Multicritical potentials and correlations

Cited by 112 publications

References 5 publications

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

Tachyon Condensation, Open-Closed Duality, Resolvents, and Minimal Bosonic and Type 0 Strings

Multiply wound Polyakov loops at strong coupling

Contact Info

Product

Resources

About