Non-perturbative defect one-point functions in planar 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: Jhep08(2020)103mentioning

confidence: 99%

Integrable boundary states in D3-D5 dCFT: beyond scalars

Kristjansen¹,

Müller²,

Zarembo

2020

“…While our draft was finalized the paper [38] appeared on the arxiv, with partially overlapping results. The paper [38] has two parts: the first calculates the 1point functions of BPS operators for the D5 system using supersymmetric localization. The second deals with non-BPS operators in the bootstrap setting.…”

Section: Jhep10(2020)123mentioning

confidence: 99%

“…We are overlapping with [38] with the calculation of the K-matrix from symmetries. Indeed our K-matrix (5.31) is equivalent to their (4.30), once we change the sign of the momentum originating from a different definition of the S-matrix and take into account that their S-matrix uses a different phase factor for bosons.…”

Section: Jhep10(2020)123mentioning

confidence: 99%

Boundary states, overlaps, nesting and bootstrapping AdS/dCFT

Gombor

Bajnok

2020

Integrable boundary states can be built up from pair annihilation amplitudes called K-matrices. These amplitudes are related to mirror reflections and they both satisfy Yang Baxter equations, which can be twisted or untwisted. We relate these two notions to each other and show how they are fixed by the unbroken symmetries, which, together with the full symmetry, must form symmetric pairs. We show that the twisted nature of the K-matrix implies specific selection rules for the overlaps. If the Bethe roots of the same type are paired the overlap is called chiral, otherwise it is achiral and they correspond to untwisted and twisted K-matrices, respectively. We use these findings to develop a nesting procedure for K-matrices, which provides the factorizing overlaps for higher rank algebras automatically. We apply these methods for the calculation of the simplest asymptotic all-loop 1-point functions in AdS/dCFT. In doing so we classify the solutions of the YBE for the K-matrices with centrally extended $$ \mathfrak{su} $$ su (2|2)c symmetry and calculate the generic overlaps in terms of Bethe roots and ratio of Gaudin determinants.

“…Important achievements have been obtained in this highly symmetric context also in presence of extended objects, like the BPS Wilson loops, that preserve part of the N = 4 superconformal symmetry [5][6][7][8] and are examples of conformal defects [9][10][11][12][13][14][15][16]. Many of these results can be efficiently derived using supersymmetric localization [17,18], which allows to reduce the calculation of the partition function on a sphere S 4 and of other observables to a computation in a Gaussian matrix model.…”

Section: Jhep09(2020)116mentioning

confidence: 99%

$$ \mathcal{N} $$ = 2 Conformal SYM theories at large $$ \mathcal{N} $$

Beccaria

Billó

Galvagno

et al. 2020

137

We consider a class of $$ \mathcal{N} $$ N = 2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere S4, which also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-N limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with N differs in the planar limit from the $$ \mathcal{N} $$ N = 4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small ’t Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed.