scholarly journals Toda Tau Functions with Quantum Torus Symmetries

10.14311/1370 ◽  
2011 ◽  
Vol 51 (2) ◽  
Author(s):  
K. Takasaki
Keyword(s):  
Topological Strings ◽  
Special Class ◽  
Gauge Theories ◽  
Free Fermion ◽  
Fermion System ◽  
Quantum Torus ◽  
Tau Functions ◽  
Toda Hierarchy ◽  
Crystal Model ◽  
Melting Crystal

The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of topological strings and 5D SUSY gauge theories. The quantum torus algebra is realized by a 2D complex free fermion system that underlies the Toda hierarchy, and exhibits mysterious “shift symmetries”. This article is based on collaboration with Toshio Nakatsu.

scholarly journals Intertwining operator and integrable hierarchies from topological strings

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jean-Emile Bourgine
Keyword(s):  
Topological Strings ◽  
Vertex Operator ◽  
Integrable Hierarchies ◽  
Kp Hierarchy ◽  
Tau Function ◽  
Time Deformation ◽  
Toroidal Algebra ◽  
Crystal Model ◽  
Melting Crystal ◽  
Definition Of

Abstract In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the underlying quantum W1+∞ symmetry. Specifically, we point out the role played by automorphisms and the connection with the intertwiner — or vertex operator — of the algebra. This algebraic perspective allows us to extend part of their derivation to the refined melting crystal model, lifting the algebra to the quantum toroidal algebra of $$ \mathfrak{gl} $$ gl (1) (also called Ding-Iohara-Miki algebra). In this way, we take a first step toward the definition of deformed hierarchies associated to A-model refined topological strings.

scholarly journals Melting Crystal, Quantum Torus and Toda Hierarchy

2008 ◽  
Vol 285 (2) ◽  
pp. 445-468 ◽  
Author(s):  
Toshio Nakatsu ◽  
Kanehisa Takasaki
Keyword(s):  
Quantum Torus ◽  
Toda Hierarchy ◽  
Melting Crystal

scholarly journals Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Pavlo Gavrylenko ◽  
Alessandro Tanzini
Keyword(s):  
Integrable System ◽  
Gauge Theories ◽  
The Self ◽  
Free Fermion ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Specific Time ◽  
Dimensional Torus ◽  
Isomonodromic Deformations ◽  
Deformation Problem

AbstractWe study the relation between class $$\mathcal {S}$$ S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual $$\Omega $$ Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding $$\tau $$ τ -function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to $$W_N$$ W N free fermion correlators on the torus.

A RENORMALIZATION GROUP APPROACH FOR MANY-FERMION PROBLEMS

1992 ◽  
Vol 06 (05n06) ◽  
pp. 749-758 ◽  
Author(s):  
R. SHANKAR
Keyword(s):  
Renormalization Group ◽  
Landau Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Free Fermion ◽  
Fermion System ◽  
Group Approach ◽  
Fermionic Systems ◽  
Renormalization Group Approach ◽  
The Stability

A renormalization group transformation (RGT) that permits us to analyze the stability of fermionic systems to various perturbations in any number of dimensions is developed. An RGT that leaves invariant the free fermion system (on or off a lattiice) is defined and interactions are classified as relevent, irrelevent or marginal. It is shown how the RGT automatically considers competing instabilities simultaneously, in contrast to mean field theory, which focuses on just one. It is shown that at weak coupling only the BCS coupling is relevent unless there is nesting. Both Landau theory and the Kohn-Luttinger argument are discussed in this context.

scholarly journals BPS States, Crystals, and Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-52 ◽  
Author(s):  
Piotr Sułkowski
Keyword(s):  
Matrix Model ◽  
Topological String ◽  
Model Representation ◽  
Free Fermion ◽  
Wall Crossing ◽  
Melting Crystal ◽  
Bps States ◽  
String Amplitudes ◽  
Calabi Yau Manifolds

We review free fermion, melting crystal, and matrix model representations of wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider both unrefined and refined BPS counting of closed BPS states involving D2- and D0-branes bound to a D6-brane, as well as open BPS states involving open D2-branes ending on an additional D4-brane. Appropriate limit of these constructions provides, among the others, matrix model representation of refined and unrefined topological string amplitudes.

scholarly journals Holographic M5 branes in AdS7 × S4

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Varun Gupta
Keyword(s):  
General Solution ◽  
Special Class ◽  
Gauge Theories ◽  
Holomorphic Functions ◽  
Boundary Region ◽  
Complex Variables ◽  
Minimal Amount ◽  
World Volume ◽  
The World ◽  
Supersymmetric Gauge

Abstract We study classical M5 brane solutions in the probe limit in the AdS7× S4 background geometry that preserve the minimal amount of supersymmetry. These solutions describe the holography of codimension-2 defects in the 6d boundary dual $$ \mathcal{N} $$ N = (0, 2) supersymmetric gauge theories. The general solution is described in terms of holomorphic functions that satisfy a scaling condition. We show the behavior of the world-volume of a special class of BPS solutions near the AdS boundary region can be characterized by general equations, which describe it as intersections of the zeros of holomorphic functions in three complex variables with a 5-sphere.

scholarly journals Ephemeral islands, plunging quantum extremal surfaces and BCFT channels

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Timothy J. Hollowood ◽  
S. Prem Kumar ◽  
Andrea Legramandi ◽  
Neil Talwar
Keyword(s):  
Black Hole ◽  
High Temperature ◽  
Special Class ◽  
Related Problem ◽  
Temperature Limit ◽  
Free Fermion ◽  
High Temperature Limit

Abstract We consider entanglement entropies of finite spatial intervals in Minkowski radiation baths coupled to the eternal black hole in JT gravity, and the related problem involving free fermion BCFT in the thermofield double state. We show that the non-monotonic entropy evolution in the black hole problem precisely matches that of the free fermion theory in a high temperature limit, and the results have the form expected for CFTs with quasiparticle description. Both exhibit rich behaviour that involves at intermediate times, an entropy saddle with an island in the former case, and in the latter a special class of disconnected OPE channels. The quantum extremal surfaces start inside the horizon, but can emerge from and plunge back inside as time evolves, accompanied by a characteristic dip in the entropy also seen in the free fermion BCFT. Finally an entropy equilibrium is reached with a no-island saddle.

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