String Theory Side Research Articles

Nonrelativistic Holography from AdS_{5}/CFT_{4}.

We show that a novel holographic correspondence appears after taking a suitable stringy nonrelativistic limit of the AdS_{5}/CFT_{4} duality. This correspondence relates string theory in string Newton-Cartan AdS_{5}×S^{5} with Galilean electrodynamics with five scalars defined on the Penrose conformal boundary. As a first test, we match the Killing vectors on the string theory side with the on-shell symmetries of the dual field theory.

On AdS/CFT duality in the twisted sector of string theory on AdS5× S5/ℤ2 orbifold background

We consider type IIB string theory on an AdS5 × S5/ℤ2 orbifold background, which should be dual to 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal SU(N) × SU(N) gauge theory with two bi-fundamental hypermultiplets. The correlator of two chiral BPS operators from the twisted sector of this quiver CFT exhibits non-trivial dependence on the ’t Hooft coupling λ already in the planar limit. This dependence was recently determined using localisation and the expansion at large λ contains a subleading contribution proportional to ζ(3)λ−3/2. We address the question of how to reproduce this correction on the string theory side by starting with the ζ(3)α′3 term in the type IIB string effective action. We find a regular solution of type IIB supergravity which represents a resolution of the AdS5 × S5/ℤ2 orbifold and demonstrate that the relevant light twisted sector states may be identified as additional supergravity 2-form modes “wrapping” a finite 2-cycle in the resolution space. Reproducing the structure of the gauge theory result becomes more transparent in the large R-charge or BMN-like limit in which the resolved background takes a pp-wave form with the transverse space being a product of ℝ4 and the Eguchi-Hanson space.

BPS Wilson loop in mathcal{N} = 2 superconformal SU(N) \u201corientifold\u201d gauge theory and weak-strong coupling interpolation

We consider the expectation value leftlangle mathcal{W}rightrangle of the circular BPS Wilson loop in mathcal{N} = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to mathcal{N} = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5× S5 superstring theory. On the string theory side leftlangle mathcal{W}rightrangle is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the mathcal{N} = 4 SYM case and in the mathcal{N} = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in leftlangle mathcal{W}rightrangle should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for leftlangle mathcal{W}rightrangle . We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

String integrability of defect CFT and dynamical reflection matrices

The D3-D5 probe-brane system is holographically dual to a defect CFT which is known to be integrable. The evidence comes mainly from the study of correlation functions at weak coupling. In the present work we shed light on the emergence of integrability on the string theory side. We do so by constructing the double row transfer matrix which is conserved when the appropriate boundary conditions are imposed. The corresponding reflection matrix turns out to be dynamical and depends both on the spectral parameter and the string embedding coordinates.

Spin Matrix theory string backgrounds and Penrose limits of AdS/CFT

Spin Matrix theory (SMT) limits provide a way to capture the dynamics of the AdS/CFT correspondence near BPS bounds. On the string theory side, these limits result in non-relativistic sigma models that can be interpreted as novel non-relativistic strings. This SMT string theory couples to non-relativistic U(1)-Galilean background geometries. In this paper, we explore the relation between pp-wave backgrounds obtained from Penrose limits of AdS5 × S5, and a new type of U(1)-Galilean backgrounds that we call flat-fluxed (FF) backgrounds. These FF backgrounds are the simplest possible SMT string backgrounds and correspond to free magnons from the spin chain perspective. We provide a catalogue of the U(1)-Galilean backgrounds one obtains from SMT limits of string theory on AdS5 × S5 and subsequently study large charge limits of these geometries from which the FF backgrounds emerge. We show that these limits are analogous to Penrose limits of AdS5 × S5 and demonstrate that the large charge/Penrose limits commute with the SMT limits. Finally, we point out that U(1)-Galilean backgrounds prescribe a symplectic manifold for the transverse SMT string embedding fields. This is illustrated with a Hamiltonian derivation for the SMT limit of a particle.

Wilson lines in AdS/dCFT

We consider the expectation value of Wilson lines in two defect versions of N=4 SYM, both with supersymmetry completely broken, where one is described in terms of an integrable boundary state, the other one not. For both cases, imposing a certain double scaling limit, we find agreement to two leading orders between the expectation values calculated from respectively the field theory- and the string theory side of the AdS/dCFT correspondence.

Antisymmetric Wilson loops in mathcal{N} = 4 SYM beyond the planar limit

We study the frac{1}{2} -BPS circular Wilson loop in the totally antisymmetric representation of the gauge group in mathcal{N} = 4 supersymmetric Yang-Mills. This observable is captured by a Gaussian matrix model with appropriate insertion. We compute the first 1/N correction at leading order in ’t Hooft coupling by means of the matrix model loop equations. Disagreement with the 1-loop effective action of the holographically dual D5-brane suggests the need to account for gravitational backreaction on the string theory side.

Probing the string winding sector

We probe a slice of the massive winding sector of bosonic string theory from toroidal compactifications of Double Field Theory (DFT). This string subsector corresponds to states containing one left and one right moving oscillators. We perform a generalized Kaluza Klein compactification of DFT on generic 2n-dimensional toroidal constant backgrounds and show that, up to third order in fluctuations, the theory coincides with the corresponding effective theory of the bosonic string compactified on n-dimensional toroidal constant backgrounds, obtained from three-point amplitudes. The comparison between both theories is facilitated by noticing that generalized diffeomorphisms in DFT allow to fix generalized harmonic gauge conditions that help in identifying the physical degrees of freedom. These conditions manifest as conformal anomaly cancellation requirements on the string theory side. The explicit expression for the gauge invariant effective action containing the physical massless sector (gravity+antisymmetric+gauge+ scalar fields) coupled to towers of generalized Kaluza Klein massive states (corresponding to compact momentum and winding modes) is found. The action acquires a very compact form when written in terms of fields carrying O(n, n) indices, and is explicitly T-duality invariant. The global algebra associated to the generalized Kaluza Klein compactification is discussed.

Interacting giant gravitons from spin matrix theory

Using the non-abelian DBI action we find an effective matrix model that describes the dynamics of weakly interacting giant gravitons wrapped on three-spheres in the AdS part of AdS_5 x S^5 at high energies with two angular momenta on the S^5. In parallel we consider the limit of \CN=4 super Yang-Mills theory near a certain unitarity bound where it reduces to the quantum mechanical theory called SU(2) Spin Matrix Theory. We show that the exact same matrix model that describes the giant gravitons on the string theory side also provides the effective description in the strong coupling and large energy limit of the Spin Matrix Theory. Thus, we are able to match non-supersymmetric dynamics of D-branes on AdS_5 x S^5 to a finite-N regime in \CN=4 super Yang-Mills theory near a unitarity bound.

Some three-point correlation functions in the η-deformed AdS5 × S5

We compute some normalized structure constants in the [Formula: see text]-deformed [Formula: see text] in the framework of the semiclassical approach. This is done for the cases when the “heavy” string states are finite-size giant magnons carrying one angular momentum and for three different choices of the “light” state: primary scalar operators, dilaton operator with nonzero momentum, singlet scalar operators on higher string levels. Since the dual field theory is still unknown, the results obtained here must be considered as conjectures or as predictions from the string theory side.

Large J expansion in ABJM theory revisited.

Recently there has been progress in the computation of the anomalous dimensions of gauge theory operators at strong coupling by making use of the AdS/CFT correspondence. On the string theory side they are given by dispersion relations in the semiclassical regime. We revisit the problem of a large-charge expansion of the dispersion relations for simple semiclassical strings in an mathrm{AdS}_4times {mathbb {CP}}^3 background. We present the calculation of the corresponding anomalous dimensions of the gauge theory operators to an arbitrary order using three different methods. Although the results of the three methods look different, power series expansions show their consistency.

Higher spin holography and the AdS string sigma model

We analyse the cubic spin-3 interaction in AdS space using the higher spin extension of the string-theoretic sigma-model constructed in our previous work, whose low energy limit is described by the AdS vacuum solution. We find that, in the leading order of the cosmological constant, the spin-3 correlator on the AdS4 string theory side reproduces the structure of the three-point function of composite operators, quadratic in free fields, in the dual d = 3 vector model. The cancellation of holography violating terms in d = 3 is related to the value of the Liouville background charge in d = 4.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

String theories on warped AdS backgrounds and integrable deformations of spin chains

We study integrable deformations of AdS/CFT by focusing upon three kinds of warped AdS_3 geometries, 1) space-like warped AdS_3, 2) time-like warped AdS_3 and 3) null warped AdS_3. These geometries are embedded into type IIB supergravity solutions and are regarded as consistent string backgrounds. By restricting the classical motion of strings on the warped AdS_3xS^1 subspace, the Landau-Lifshitz sigma models are derived by taking the fast-moving limit. The first two warped AdS_3 spaces correspond to anisotropic deformations of the sl(2) spin chain and the last one to Jordanian deformations. After taking the continuum limit of the deformed spin chains with coherent states, the resulting theories agree with the Landau-Lifshitz sigma models obtained from the string-theory side.

Six and seven loop Konishi from Lüscher corrections

Abstract In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Lüscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on the string theory side, or with direct gauge theory computations. The seven loop level is the theoretical limit of this Lüscher approach as at eight loops double-wrapping corrections will appear.

Three-point functions of BMN operators at weak and strong coupling II. One loop matching

In a previous paper, arXiv:1204.3096, we have shown that the fully dynamical three-point correlation functions of BMN operators are identical at the tree level in the planar limit of perturbative field theory and, on the string theory side, calculated by means of the Dobashi-Yoneya three string vertex in the Penrose limit. Here we present a one-loop calculation of the same quantity both on the field-theory and string-theory side, where a complete identity between the two results is demonstrated.

Holographic 3-point function at one loop

We explore the recent weak/strong coupling match of three-point functions in the AdS/CFT correspondence for two semi-classical operators and one light chiral primary operator found by Escobedo et al. This match is between the tree-level three-point function with the two semi-classical operators described by coherent states while on the string side the three-point function is found in the Frolov-Tseytlin limit. We compute the one-loop correction to the three-point function on the gauge theory side and compare this to the corresponding correction on the string theory side. We find that the corrections do not match. Finally, we discuss the possibility of further contributions on the gauge theory side that can alter our results.

Three Point Tree Level Amplitude in Superstring Theory

In order to check the definite amplitude and the exact zero result of the amplitude of three massless points $(CAA)$ in both string theory and field theory side for $p=n$ case and to find all gauge field couplings to R-R closed string, we investigate the disk level S-matrix element of one Ramond-Ramond field and two gauge field vertex operators in the world volume of BPS branes.

Analytic results for MHV Wilson loops

We obtain concise analytic formulae for Wilson loops computed on special n-point polygonal contours through two-loops in weakly coupled \( \mathcal{N} = 4 \) supersymmetric gauge theory. The contours we consider can be embedded into a (1 + 1)-dimensional subspace of the 4-dimensional gauge theory, corresponding to the boundary of the AdS 3 on the string theory side. Our analytic results hold for any number of edges, thus generalising to arbitrary n the recently derived expressions for 2-dimensional octagons. These polygonal Wilson loops have been conjectured to be equivalent to MHV scattering amplitudes in planar \( \mathcal{N} = 4 \) SYM.

Giant magnons in symmetric spaces: explicit N-soliton solutions for CP n , SU(n) and S n

Giant magnons are one of the main manifestations of integrability on the string theory side of the AdS/CFT correspondence. Motivated by the recent advances in their study, especially in the context of the string theory dual of ABJM theory, we present and prove explicit N-soliton solutions for the relevant CP^n, SU(n) and S^n sigma models. The proof is based on solving the dressing method recursion with the help of determinant operations, and our solutions hold for any choice of vacuum and soliton parameters. We further specialize our results for the choices that lead to giant magnons, and as an application, we calculate the classical time delay due to the scattering of an arbitrary number of CP^2 elementary dyonic magnons. The determinant expressions for our N-soliton solutions could possibly be used for the derivation of an effective particle description of magnon scattering.

Holographic conformal window — a bottom up approach

We propose a five-dimensional framework for modeling the background geometry associated to ordinary Yang-Mills (YM) as well as to nonsupersymmetric gauge theories possessing an infrared fixed point with fermions in various representations of the underlying gauge group. The model is based on the improved holographic approach, on the string theory side, and on the conjectured all-orders beta function for the gauge theory one. We first analyze the YM gauge theory. We then investigate the effects of adding flavors and show that, in the holographic description of the conformal window, the geometry becomes AdS when approaching the ultraviolet and the infrared regimes. As the number of flavors increases within the conformal window we observe that the geometry becomes more and more of AdS type over the entire energy range.