Taming defects in $$ \mathcal{N} $$ = 4 super-Yang-Mills

A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the gauge group jumps by k units across a domain wall. The one-point functions of local operators in this setup map to overlaps between on-shell Bethe states in the underlying spin chain and a boundary state representing the D5 brane. Focussing on the k = 1 case, we extend the construction to gluonic and fermionic sectors, which was prohibitively difficult for k > 1. As a byproduct, we test an all-loop proposal for the one-point functions in the su(2) sector at the half-wrapping order of perturbation theory.

Section: Jhep08(2020)103mentioning

confidence: 90%

Section: Protected Operators and Wrappingmentioning

confidence: 99%

Integrable boundary states in D3-D5 dCFT: beyond scalars

Kristjansen¹,

Müller²,

Zarembo

2020

“…There are, however, other tight and direct links between q-deformed two-dimensional Yang-Mills theory and four-dimensional supersymmetric Yang-Mills theory, for example in the equivalence with the superconformal index [87] in the context of Gaiotto's 4d/2d dualities [88]. Two-dimensional Yang-Mills theory and its deformations appear as well from direct localization computations on the four-sphere S 4 [89][90][91] and on the four-dimensional hemisphere [92], possibly with the inclusion of defects [93]. as a q-deformation of b ∞ , and b ∞ is correctly recovered in the limit (3.4).…”

Section: Jhep11(2020)086mentioning

confidence: 99%

$$ T\overline{T} $$-deformation of q-Yang-Mills theory

Santilli

Szabo

Tierz

2020

We derive the $$ T\overline{T} $$ T T ¯ -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $$ T\overline{T} $$ T T ¯ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the $$ T\overline{T} $$ T T ¯ -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

“…The defect CFT defined by the 1/2-BPS Wilson loop contains a supersymmetric subsector whose correlation functions are position-independent [23,24,52,[67][68][69]. For the Wilson loops in the fundamental representation, such correlators were computed exactly using the supersymmetric localization 4 in [23,24].…”

Section: /8 Bps Wilson Loops and Topological Sectormentioning

confidence: 99%

“…We used a normal ordering symbol : • : to emphasize the absence of the self-contractions within each operator. One important feature of these correlation functions is their position-independence, which follows from the fact that the spatial translation ofΦ(x) is Q-exact [67,69]. In the rest of this paper, we often denote these operators bỹ…”

Section: /8 Bps Wilson Loops and 2dmentioning

confidence: 99%

Giant Wilson loops and AdS2/dCFT1

Giombi

Jiang

Komatsu

2020

The 1/2-BPS Wilson loop in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS2× S2 and AdS2× S4 worldvolume geometries, ending at the AdS5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.