We consider scalar local operators of the determinant type in the conformal “fishnet” theory that arises as a limit of gamma-deformed   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory. We generalise a field-theory approach to expand their correlation functions to arbitrary order in the small coupling constants and apply it to the bi-scalar reduction of the model. We explicitly analyse the two-point functions of determinants, as well as of certain deformations with the insertion of scalar fields, and describe the Feynman-graph structure of three- and four-point correlators with single-trace operators. These display the topology of globe and spiral graphs, which are known to renormalise single-trace operators, but with “alternating” boundary conditions. In the appendix material we further investigate a four-point function of two determinants and the shortest bi-local single trace. We resum the diagrams by the Bethe-Salpeter method and comment on the exchanged OPE states.

United Kingdom

Omar Shahpo

Sweden

Edoardo Vescovi

Correlation functions of determinant operators in conformal fishnet theory

We calculate the four-point function of <math><mn>1</mn><mo>/</mo><mn>2</mn></math>-BPS (Bogomolnyi–Prasad–Sommerfield) determinant operators in <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM (super Yang-Mills) at next-to-leading order at weak coupling. We use two complementary methods recently developed for a class of determinant three-point functions: one is based on Feynman diagrams and it extracts perturbative data at finite <math><mi>N</mi></math>, while the other one expresses a generic correlator of determinants as the zero-dimensional integral over an auxiliary matrix field. We generalize the latter approach to calculate one-loop corrections and we solve the four-point function in a semiclassical approach at large <math><mi>N</mi></math>. The results allow us to comment on the order of the phase transition that the four-point function is expected to exhibit in an exact integrability-based description.

Four-point function of determinant operators in <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM

We develop a novel nonperturbative approach to a class of three-point functions in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS5 ×S5. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large N collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization of g-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-state g-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.

CERN

Yunfeng Jiang

United States

Shota Komatsu

Structure constants in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM at finite coupling as worldsheet g-function

We introduce a nonperturbative approach to correlation functions of two determinant operators and one nonprotected single-trace operator in planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Yang-Mills theory. Based on the gauge-string duality, we propose that they correspond to overlaps on the string world sheet between an integrable boundary state and a state dual to the single-trace operator. We determine the boundary state using the symmetry and integrability of the dual superstring <math><mi>σ</mi></math> model and write expressions for the correlators at finite coupling, which we conjecture to be valid for operators of arbitrary size. The proposal is put to the test at weak coupling.

Exact Three-Point Functions of Determinant Operators in Planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> Supersymmetric Yang-Mills Theory

In this paper we study the expectation value of deformations of the circular Wilson loop in   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$  super Yang-Mills theory. The leading order deformation, known as the Bremsstrahlung function, can be obtained exactly from supersymmetric localization, so our focus is on deformations at higher orders. We find simple expressions for the expectation values for generic deformations at the quartic order at one-loop at weak coupling and at leading order at strong coupling. We also present a very simple algorithm (not requiring integration) to evaluate the two-loop result. We find that an exact symmetry of the strong coupling sigma-model, known as the spectral-parameter independence, is an approximate symmetry at weak coupling, modifying the expectation value starting only at the sextic order in the deformation. Furthermore, we find very simple patterns for how the spectral parameter can appear in the weak coupling calculation, suggesting all-order structures.

Michael Cooke

Amit Dekel

Nadav Drukker

Brazil

Diego Trancanelli

Deformations of the circular Wilson loop and spectral (in)dependence

In this paper we study the Bremsstrahlung functions for the  <math><mfrac><mn>1</mn><mn>6</mn></mfrac><mi>B</mi><mi>P</mi><mi>S</mi></math> $$ \frac{1}{6}\mathrm{B}\mathrm{P}\mathrm{S} $$ and the  <math><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>B</mi><mi>P</mi><mi>S</mi></math> $$ \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} $$ Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric (B 1/6 φ ) and R-symmetry (B 1/6 θ ) deformations of the  <math><mfrac><mn>1</mn><mn>6</mn></mfrac><mi>B</mi><mi>P</mi><mi>S</mi></math> $$ \frac{1}{6}\mathrm{B}\mathrm{P}\mathrm{S} $$ Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for B 1/6 θ  based on a known result for B 1/6 φ . Subsequently, we explore the consequences of this relation for the  <math><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>B</mi><mi>P</mi><mi>S</mi></math> $$ \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} $$ Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function h(λ). During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.

Germany

Lorenzo Bianchi

France

Michelangelo Preti

Exact Bremsstrahlung functions in ABJM theory

We consider antiparallel Wilson lines in N $$ \mathcal{N} $$ = 4 super Yang-Mills in the presence of a codimension-1 defect. We compute the Wilson lines’ expectation value both at weak coupling, in the gauge theory, and at strong coupling, by finding the string configurations which are dual to this operator. These configurations display a Gross-Ooguri transition between a connected, U-shaped string phase and a phase in which the string breaks into two disconnected surfaces. We analyze in detail the critical configurations separating the two phases and compare the string result with the gauge theory one in a certain double scaling limit.

Quark-antiquark potential in defect conformal field theory

We compute the null cusp anomalous dimension of ABJM theory at strong coupling up to two-loop order. This is done by evaluating corrections to the corresponding superstring partition function, weighted by the AdS 4 × ℂℙ 3 action in AdS light-cone gauge. We compare our result, where we use an anomalous shift in the AdS 4 radius, with the cusp anomaly of N $$ \mathcal{N} $$ = 4 SYM, and extract the two-loop contribution to the non-trivial integrable coupling h (λ) of ABJM theory. It coincides with the strong coupling expansion of the exact expression for h (λ) recently conjectured by Gromov and Sizov. Our work provides thus a non-trivial perturbative check for the latter, as well as evidence for two-loop UV-finiteness and quantum integrability of the Type IIA AdS 4 × ℂℙ 3 superstring in this gauge.