scholarly journals Subleading corrections in $$ \mathcal{N} $$ = 3 Gaiotto-Tomasiello theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
James T. Liu ◽  
Robert J. Saskowski
Keyword(s):  
Free Energy ◽  
Perturbative Expansion ◽  
Genus Zero ◽  
Gauge Groups ◽  
Contour Integrals ◽  
Full Expression

Abstract We study subleading corrections to the genus-zero free energy of the $$ \mathcal{N} $$ N = 3 Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar resolvent, up to exponentially suppressed corrections. In the particular case that the two gauge groups in the quiver are of equal rank, we find an explicit (perturbative) expansion for the free energy. If, additionally, both groups have equal levels, then we find the full expression for the genus-zero free energy, modulo exponentially suppressed corrections. We also verify our results numerically.

VORTICES IN HIGH-TEMPERATURE STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1063-1067 ◽  
Author(s):  
G. CHAPLINE ◽  
F.R. KLINKHAMER
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
High Temperature ◽  
String Theory ◽  
High Temperatures ◽  
World Sheet ◽  
Genus Zero ◽  
Mass Gap ◽  
The World

We discuss the role of XY-like vortices on the world-sheet for the free energy of strings at high temperatures. There is a Kosterlitz-Thouless phase transition at the Hagedorn temperature, above which the vortices contribute to the free energy in genus zero and generate a mass gap. We speculate that high-temperature “string” theory could be essentially discrete.

THE (ORBIFOLD) EULER CHARACTERISTIC OF THE MODULI SPACE OF CURVES AND THE CONTINUUM LIMIT OF PENNER'S CONNECTED GENERATING FUNCTION

1991 ◽  
Vol 03 (03) ◽  
pp. 285-300 ◽  
Author(s):  
NOUREDDINE CHAIR
Keyword(s):  
Free Energy ◽  
Matrix Models ◽  
Euler Characteristic ◽  
Generating Function ◽  
Moduli Space ◽  
Continuum Limit ◽  
Recursion Relation ◽  
Moduli Space Of Curves ◽  
Genus Zero ◽  
The Continuum

The generating function that gives rise to the orbifold Euler characteristic of the moduli space of punctured compact Rieman surfaces [Formula: see text], g ≥ 0 is derived explicitly. In the derivation, we show that we do not need to use the three-term recursion relation for the orthogonal polynomials. Also the continuum limit of Penner's connected generating function is considered and is shown to be formally equivalent to the free energy obtained recently by Distler and Vafa which exhibits the logarithmic divergences found for genus zero and one in D = 1 matrix models. Finally, it is shown that the free energy and its s-derivatives are nothing but the continuum limit of a certain generating function introduced by Harer and Zagier in obtaining the true Euler characteristic with any number of punctures,[Formula: see text], s ≥ 0.

c = 1 − 6(n − 1)2/n, THEORIES COUPLED TO GRAVITY: A COMMENT ON THEIR POSSIBLE LATTICE MODELS REALIZATIONS

1991 ◽  
Vol 06 (18) ◽  
pp. 1709-1719 ◽  
Author(s):  
HUBERT SALEUR
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Potts Model ◽  
Planar Graphs ◽  
Critical Line ◽  
Central Charge ◽  
Lattice Models ◽  
Genus Zero ◽  
Regular Lattices ◽  
Beraha Numbers

We discuss the recently proposed logarithmic violation of scaling for c = 1 − 6(n − 1)2/n theories in the light of lattice models. We study for this purpose the Q state Potts model in its antiferromagnetic regime eK − 1 = −Q1/2, coupled to gravity. Setting Q1/2 = 2 cos π/t, this model is known to have a generic central charge c = 1 − 6(t − 1)2/t. Summing over all possible planar graphs allows us to make connection with Kostov's solution of IRF models, and to calculate the genus zero properties along the critical line. Except for n = 1, 2 we do not get indications of logarithmic violations. The apparent regularity of the thermodynamic properties (γ str = −(n − 1) = integer ) is explained by a discontinuity of the free energy of the Potts model when Q crosses the Beraha numbers [Formula: see text], n ≥ 3 in the antiferromagnetic region. Such behavior was recently observed for some regular lattices. The logarithmic terms for n = 2, c = −2 appear simply because a derivative with respect to Q has to be taken to define a non-vanishing partition function. Only the n = 1, c = 1 logarithmic terms seem to have a non-trivial origin.

scholarly journals Genus expansion of open free energy in 2d topological gravity

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Kazumi Okuyama ◽  
Kazuhiro Sakai
Keyword(s):  
Free Energy ◽  
Riemann Surfaces ◽  
Two Dimensions ◽  
Intersection Theory ◽  
Genus Zero ◽  
Kdv Hierarchy ◽  
Kdv Equations ◽  
Higher Genus ◽  
Topological Gravity ◽  
Genus Expansion

Abstract We study open topological gravity in two dimensions, or, the intersection theory on the moduli space of open Riemann surfaces initiated by Pandharipande, Solomon and Tessler. The open free energy, the generating function for the open intersection numbers, obeys the open KdV equations and Buryak’s differential equation and is related by a formal Fourier transformation to the Baker-Akhiezer wave function of the KdV hierarchy. Using these properties we study the genus expansion of the free energy in detail. We construct explicitly the genus zero part of the free energy. We then formulate a method of computing higher genus corrections by solving Buryak’s equation and obtain them up to high order. This method is much more efficient than our previous approach based on the saddle point calculation. Along the way we show that the higher genus corrections are polynomials in variables that are expressed in terms of genus zero quantities only, generalizing the constitutive relation of closed topological gravity.

scholarly journals Strong coupling expansion of free energy and BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal models with fundamental hypermultiplets

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
M. Beccaria ◽  
G. V. Dunne ◽  
A. A. Tseytlin
Keyword(s):  
Free Energy ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Expansion ◽  
Gauge Groups ◽  
Hooft Coupling ◽  
Link Type ◽  
Rank 2 ◽  
Strong Coupling Expansions ◽  
Differential Relations

Abstract As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $$ \mathcal{N} $$ N = 2 4d superconformal models we consider two special theories with gauge groups SU(N) and Sp(2N). They contain N-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $$ \mathcal{N} $$ N = 4 SYM theories. These $$ \mathcal{N} $$ N = 2 theories can be realised on a system of N D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of AdS5 × S5 superstring. Starting with the localization matrix model representation for the $$ \mathcal{N} $$ N = 2 partition function on S4 we find exact differential relations between the 1/N terms in the corresponding free energy F and the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W and also compute their large ’t Hooft coupling (λ » 1) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable Sp(2N) case we find an exact resummed expression for the leading strong coupling terms at each order in the 1/N expansion. We also determine the exponentially suppressed at large λ contributions to the non-planar corrections to F and $$ \left\langle \mathcal{W}\right\rangle $$ W and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

Encultured minds, not error reduction minds

2020 ◽  
Vol 43 ◽  
Author(s):  
Robert Mirski ◽  
Mark H. Bickhard ◽  
David Eck ◽  
Arkadiusz Gut
Keyword(s):  
Free Energy ◽  
Error Reduction ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Current Article

Abstract There are serious theoretical problems with the free-energy principle model, which are shown in the current article. We discuss the proposed model's inability to account for culturally emergent normativities, and point out the foundational issues that we claim this inability stems from.

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