Dilogarithm ladders from Wilson loops

We consider a light-like Wilson loop in N = 4 SYM evaluated on a regular n-polygon contour. Sending the number of edges to infinity the polygon approximates a circle and the expectation value of the light-like WL is expected to tend to the localization result for the circular one. We show this explicitly at one loop, providing a prescription to deal with the divergences of the light-like WL and the large n limit. Taking this limit entails evaluating certain sums of dilogarithms which, for a regular polygon, evaluate to the same constant independently of n. We show that this occurs thanks to underlying dilogarithm identities, related to the so-called “polylogarithm ladders”, which appear in rather different contexts of physics and mathematics and enable us to perform the large n limit analytically.Instituto de Física La Plat

Current-current deformations, conformal integrals and correlation functions

Motivated by the recent work on TT¯ -type deformations of 2D CFTs, a especial class of single-trace deformations of AdS3/CFT2 correspondence has been investigated. From the worldsheet perspective, this corresponds to a marginal deformation of the σ - model on AdS3 that yields a string background that interpolates between AdS3 and a flat linear dilaton solution. Here, with the intention of studying this worldsheet CFT further, we consider it in the presence of a boundary. In a previous paper, we computed different correlation functions of this theory on the disk, including the bulk 1-point function, the boundary-boundary 2-point function, and the bulk-boundary 2-point function. This led us to compute the anomalous dimension of both bulk and boundary vertex operators, which first required a proper regularization of the ultraviolet divergences of the conformal integrals. Here, we extend the analysis by computing the bulk-bulk 2-point function on the disk and other observables on the sphere. We prove that the renormalization of the vertex operators proposed in our previous works is consistent with the form of the sphere N -point functions.Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Leoni Olivera, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

Spin chain integrability in non-supersymmetric Wilson loops

We study the 1-loop dilatation operator for insertions of composite operators in a generalized Wilson loop in N = 4 super Yang-Mills, which interpolates between the supersymmetric Wilson-Maldacena loop and the ordinary Wilson loop with no scalar coupling. For SO(6) scalar insertions, we show that the 1-loop dilatation operator is integrable for the endpoints of the interpolation, i.e. either for the Wilson-Maldacena or the ordinary Wilson loop. Moreover, we also show that integrability persists for SU(2|3) insertions in the ordinary Wilson loop, even when the term making the spin chain length dynamical is included.Instituto de Física La Plat

ABJM amplitudes and WL at finite N

We evaluate ABJM observables at two loops, for any value of the rank N of the gauge group. We compute the color subleading contributions to the four-point scattering amplitude in ABJM at two loops. Contrary to the four dimensional case, IR divergent N-subleading contributions are proportional to leading poles in the regularization parameter. We then exploit the non-planar calculation for the amplitude to derive an expression for the two-loop Sudakov form factor at any N. In the planar limit the result coincides with the one recently obtained in literature by using Feynman diagrams and unitarity. Finally, we analyze the subleading contributions to the light-like four-cusps Wilson loop and interpret the result in terms of the non-abelian exponentiation theorem. All these perturbative results satisfy the uniform transcendentality principle, hinting at its validity in ABJM beyond the planar limit.Fil: Bianchi, Marco. Humboldt-Universität zu Berlin; AlemaniaFil: Leoni, Marta. Universita Degli Studi Di Milano; Italia. Istituto Nazionale di Fisica Nucleare; ItaliaFil: Leoni Olivera, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Mauri, Andrea. Universita Degli Studi Di Milano; Italia. Istituto Nazionale di Fisica Nucleare; ItaliaFil: Penati, Silvia. Universita Degli Studi Di Milano; Italia. Istituto Nazionale di Fisica Nucleare; ItaliaFil: Santambrogio, Alberto. Istituto Nazionale di Fisica Nucleare; Itali

Spin chain integrability in non-supersymmetric Wilson loops

We study the 1-loop dilatation operator for insertions of composite operators in a generalized Wilson loop in N = 4 super Yang-Mills, which interpolates between the supersymmetric Wilson-Maldacena loop and the ordinary Wilson loop with no scalar coupling. For SO(6) scalar insertions, we show that the 1-loop dilatation operator is integrable for the endpoints of the interpolation, i.e. either for the Wilson-Maldacena or the ordinary Wilson loop. Moreover, we also show that integrability persists for SU(2|3) insertions in the ordinary Wilson loop, even when the term making the spin chain length dynamical is included.Instituto de Física La Plat

Dilogarithm ladders from Wilson loops

We consider a light-like Wilson loop in N = 4 SYM evaluated on a regular n-polygon contour. Sending the number of edges to infinity the polygon approximates a circle and the expectation value of the light-like WL is expected to tend to the localization result for the circular one. We show this explicitly at one loop, providing a prescription to deal with the divergences of the light-like WL and the large n limit. Taking this limit entails evaluating certain sums of dilogarithms which, for a regular polygon, evaluate to the same constant independently of n. We show that this occurs thanks to underlying dilogarithm identities, related to the so-called “polylogarithm ladders”, which appear in rather different contexts of physics and mathematics and enable us to perform the large n limit analytically.Instituto de Física La Plat

Hairy black holes sourced by a conformally coupled scalar field in D dimensions

There exist well-known no-hair theorems forbidding the existence of hairy black hole solutions in general relativity coupled to a scalar conformal field theory in asymptotically flat space. Even in the presence of cosmological constant, where no-hair theorems can usually be circumvented and black holes with conformal scalar hair were shown to exist in D ≤ 4 dimensions, no-go results were reported for D > 4 . In this paper we prove that these obstructions can be evaded and we answer in the affirmative a question that remained open: Whether hairy black holes do exist in general relativity sourced by a conformally coupled scalar field in arbitrary dimensions. We find the analytic black hole solution in arbitrary dimension D > 4 , which exhibits a backreacting scalar hair that is regular everywhere outside and on the horizon. The metric asymptotes to (anti-)de Sitter spacetime at large distance and admits spherical horizon as well as horizon of a different topology. We also find analytic solutions when higher-curvature corrections O ( R n ) of arbitrary order n are included in the gravity action.Instituto de Física La Plat

A twisted FZZ-like dual for the 2D black hole

We study the duality between string theory formulated on a curved exact background (the two-dimensional black hole) and string theory in flat space with a tachyon-like potential. We generalize previous results on this subject by discussing a twisted version of the Fateev-Zamolodchikov-Zamolodchikov conjecture (FZZ). This duality is shown to hold at the level of N-point correlation functions on the sphere topology, and connects tree-level string amplitudes in the Euclidean version of the 2D black hole to correlation functions in a nonlinear sigma-model in flat space but in presence of a tachyon wall potential and a linear dilaton. The dual CFT we propose here corresponds to the perturbed 2D quantum gravity coupled to c < 1 matter, where the operator that describes the tachyon-like potential can be seen as an n = 2 momentum mode perturbation, while the usual sine-Liouville potential involved in the FZZ duality would correspond to the vortex sector n = 1. We give a precise prescription for computing correlation functions in the twisted model. © 2008 Polish Scientific Publishers PWN, Warszawa.Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Abdus Salam International Centre for Theoretical Pysics; ItaliaFil: Leoni Olivera, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

An exact limit of the Aharony-Bergman-Jafferis-Maldacena theory

We study planar Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in a limit where one coupling is negligible compared to the other. We provide a recipe for exactly solving the expectation value of bosonic Bogomol'nyi-Prasad-Sommerfield (BPS) Wilson loops on arbitrary smooth contours, or the leading divergence for cusped ones, using results from localization. As an application, we compute the exact (generalized) cusp anomalous dimension and Bremsstrahlung function and use it to determine the interpolating h-function. We finally prove a conjecture on the exact form of the dilatation operator in a closed sector, hinting at the integrability of this limit.Fil: Bianchi, Marco S.. Queen Mary, University Of London; Reino UnidoFil: Leoni Olivera, Matías. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin