Fishnet four-point integrals: integrable representations and thermodynamic limits
TLDR
In this paper, the authors consider four-point integrals arising in the planar limit of the conformal "fishnet" theory in four dimensions and prove the equivalence of all these representations using exact summation and integration techniques.Abstract:
We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS3 × S1, in a generalized scaling combining the thermodynamic and short-distance limits.read more
Citations
More filters
Journal ArticleDOI
Feynman polytopes and the tropical geometry of UV and IR divergences
TL;DR: In this article , a class of polytopes was introduced to concisely capture the structure of UV and IR divergences of general Feynman integrals in Schwinger parameter space, treating them in a unified way as worldline segments shrinking and expanding at different relative rates.
Journal ArticleDOI
The SAGEX review on scattering amplitudes Chapter 9: Integrability of amplitudes in fishnet theories
TL;DR: In this paper , the authors discuss the properties of scattering amplitudes in a conformal bi-scalar fishnet theory that previously appeared in the study of integrable deformations of N=4 SYM.
Journal ArticleDOI
Nonperturbative negative geometries: amplitudes at strong coupling and the amplituhedron
TL;DR: In this paper , the amplituhedron is defined for the simple case of four-particle scattering, given as a sum over complementary negative geometries, which provides a natural geometric understanding of the exponentiation of infrared (IR) divergences, as well as a new geometric definition of an IR finite observable.
Journal ArticleDOI
Ten dimensional symmetry of $$ \mathcal{N} $$ = 4 SYM correlators
TL;DR: In this paper , the authors conjecture that all loop corrections derive from an integrand which enjoys a ten-dimensional symmetry, which combines spacetime and R-charge transformations, and extend the correlator/amplitude duality by equating large R charge octagons with Coulomb branch scattering amplitudes.
References
More filters
Journal ArticleDOI
Strings in flat space and pp waves from Script N = 4 Super Yang Mills
TL;DR: In this paper, the string spectrum in flat space and pp-waves arises from the large-N limit, at fixed g2YM, of U(N) = 4 super Yang Mills.
Posted Content
Quantum Inverse Scattering Method and Correlation Functions
TL;DR: In this article, a detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well as main models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models.
Proceedings ArticleDOI
Strings in flat space and pp waves from N = 4 Super Yang Mills
TL;DR: In this article, the string spectrum in flat space and pp-waves arises from the large N limit, at fixed gYM2, of U(N) N = 4 super Yang Mills.
Journal ArticleDOI
Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills
TL;DR: In this paper, the string spectrum in flat space and pp-waves arises from the large $N$ limit, at fixed $g^2YM}$, of U(N) ${\cal N} =4$ super Yang Mills.
Journal ArticleDOI
2D gravity and random matrices
TL;DR: In this article, the authors review recent progress in 2D gravity coupled to d < 1 conformal matter, based on a representation of discrete gravity in terms of random matrices and discuss the saddle point approximation for these models, including a class of related O(n) matrix models.