Double scaling limits in gauge theories and matrix models

Bertoldi, Gaetano; Hollowood, Timothy J.; Miramontes, J. Luis

doi:10.1088/1126-6708/2006/06/045

Cited by 8 publications

(41 citation statements)

References 80 publications

(174 reference statements)

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“…[28] for a recent example with references to the literature). 1 In that case one studies type B topological string theory on Calabi-Yau backgrounds related to the deformed conifold.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions, double-scaling limit, and topological strings

Caporaso¹,

et al. 2007

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Topological strings on Calabi-Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi-Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q-deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q-deformed 2D Yang-Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2D gravity. We give strong evidence that there is a double-scaled theory at the critical point whose all-genus free energy is governed by the Painlevé I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2D supergravity, and we comment on possible implications for nonperturbative 2D gravity. We also give evidence for a new open/closed duality relating these Calabi-Yau backgrounds to open strings with framing.

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“…[28] for a recent example with references to the literature). 1 In that case one studies type B topological string theory on Calabi-Yau backgrounds related to the deformed conifold.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions, double-scaling limit, and topological strings

Caporaso¹,

et al. 2007

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“…It was shown in [4], generalizing a result of [3], that in the limit a → 0, in its sense as a complex manifold, the curve Σ factorizes as Σ − ∪ Σ + . The complement to the near-critical curve is of the form Σ + :…”

Section: The Matrix Model Double-scaling Limitmentioning

confidence: 83%

“…It is important to stress that the above singularities are obtained on shell [3,4]. In the context of supersymmetric gauge theories, the moduli {S i } are fixed by extremizing the glueball superpotential (2.7).…”

Section: Engineering the Double-scaling Limit On-shellmentioning

confidence: 99%

“…It is not, a priori , clear whether a double-scaling limit can be reached whilst simultaneously being on-shell with respect to the glueball superpotential. We will now review the analysis of [3,4] and show that suitable choices of the coupling constants {g i } do indeed allow for a double-scaling limit on-shell with respect to the glueball superpotential. In general, the potentials required are nonminimal.…”

Section: Engineering the Double-scaling Limit On-shellmentioning

confidence: 99%

“…In [3,4], the large N limit of a wide class of four-dimensional N = 1 theories in a partially confining phase was studied. It was found that the low-energy description of the theory breaks down close to points in the parameter space where some baryonic and/or mesonic states become massless.…”

Section: Introductionmentioning

confidence: 99%

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LargeNgauge theories and topological cigars

Bertoldi¹,

Hollowood²

2007

J. High Energy Phys.

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We analyze the conjectured duality between a class of double-scaling limits of a one-matrix model and the topological twist of non-critical superstring backgrounds that contain the N = 2 Kazama-Suzuki SL(2)/U(1) supercoset model. The untwisted backgrounds are holographically dual to double-scaled Little String Theories in four dimensions and to the large N double-scaling limit of certain supersymmetric gauge theories. The matrix model in question is the auxiliary Dijkgraaf-Vafa matrix model that encodes the F-terms of the above supersymmetric gauge theories. We evaluate matrix model loop correlators with the goal of extracting information on the spectrum of operators in the dual non-critical bosonic string. The twisted coset at level one, the topological cigar, is known to be equivalent to the c = 1 non-critical string at self-dual radius and to the topological theory on a deformed conifold. The spectrum and wavefunctions of the operators that can be deduced from the matrix model double-scaling limit are consistent with these expectations.

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Entanglement wedge cross section from CFT: dynamics of local operator quench

Kusuki

Tamaoka

2020

J. High Energ. Phys.

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We derive dynamics of the entanglement wedge cross section from the reflected entropy for local operator quench states in the holographic CFT. By comparing between the reflected entropy and the mutual information in this dynamical setup, we argue that (1) the reflected entropy can diagnose a new perspective of the chaotic nature for given mixed states and (2) it can also characterize classical correlations in the subregion/subregion duality. Moreover, we point out that we must improve the bulk interpretation of a heavy state even in the case of well-studied entanglement entropy. Finally, we show that we can derive the same results from the odd entanglement entropy. The present paper is an extended version of our earlier report arXiv:1907.06646 and includes many new results: non-perturbative quantum correction to the reflected/odd entropy, detailed analysis in both CFT and bulk sides, many technical aspects of replica trick for reflected entropy which turn out to be important for general setup, and explicit forms of multi-point semi-classical conformal blocks under consideration.

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Double scaling limits in gauge theories and matrix models

Cited by 8 publications

References 80 publications

Phase transitions, double-scaling limit, and topological strings

Phase transitions, double-scaling limit, and topological strings

LargeNgauge theories and topological cigars

Entanglement wedge cross section from CFT: dynamics of local operator quench

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