Thermodynamic Bethe Ansatz for Biscalar Conformal Field Theories in any Dimension

Self Cite

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.

Section: Introductionmentioning

confidence: 87%

Section: Integral Representationsmentioning

confidence: 99%

Fishnet four-point integrals: integrable representations and thermodynamic limits

Basso

Dixon

Kosower

et al. 2021

Self Cite

“…SoV-type methods adapted to the principal series representations have already led to a variety of interesting results in this context [70][71][72][73] (see also [74]).…”

Section: Jhep05(2021)169mentioning

confidence: 99%

Determinant form of correlators in high rank integrable spin chains via separation of variables

Gromov

Levkovich-Maslyuk

Ryan

2021

In this paper we take further steps towards developing the separation of variables program for integrable spin chains with $$ \mathfrak{gl}(N) $$ gl N symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to compute correlation functions and wave function overlaps in a simple determinant form. In particular, we show how an overlap between on-shell and off-shell algebraic Bethe states can be written as a determinant. Another result, particularly useful for AdS/CFT applications, is an overlap between two Bethe states with different twists, which also takes a determinant form in our approach. Our results also extend our previous works in collaboration with A. Cavaglia and D. Volin to general values of the spin, including the SoV construction in the higher-rank non-compact case for the first time.

“…The last example we consider is provided by the biscalar fishnet model introduced in [87], and studied further in [18][19][20][88][89][90] (see also the review [91]).…”

Section: Jhep05(2021)004mentioning

confidence: 99%

Instability of complex CFTs with operators in the principal series

Benedetti

2021

We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.