arXiv subjects

Andrea Fontanella

Publications and source records attributed to Andrea Fontanella.

22 records · Page 2Linked to original sources

arXiv2019

Geometry of Massless Scattering in Integrable Superstring

We consider the action of the $q$-deformed Poincaré superalgebra on the massless non-relativistic R-matrix in ordinary (undeformed) integrable $AdS_2 \times S^2 \times T^6$ type IIB superstring theory. The boost generator acts non-trivially on the R-matrix, confirming the existence of a non-relativistic rapidity $γ$ with respect to which the R-matrix must be of difference form. We conjecture that from a massless AdS/CFT integrable relativistic R-matrix one can obtain the parental massless non-relativistic R-matrix simply by replacing the relativistic rapidity with $γ$. We check our conjecture in ordinary (undeformed) $AdS_n \times S^n \times T^{10 - 2n}$, $n = 2, 3$. In the case $n=3$, we check that the matrix part and the dressing factor - up to numerical accuracy for real momenta - obey our prescription. In the $n=2$ case, we check the matrix part and propose the non-relativistic dressing factor. We then start a programme of classifying R-matrices in terms of connections on fibre bundles. The conditions obtained for the connection are tested on a set of known integrable R-matrices.

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arXiv2018

Black Horizons and Integrability in String Theory

This thesis is devoted to the study of geometric aspects of black holes and integrable structures in string theory. In the first part, symmetries of the horizon and its bulk extension will be investigated. We investigate the horizon conjecture beyond the supergravity approximation, by considering α' corrections of heterotic supergravity in perturbation theory, and show that standard global techniques can no longer be applied. A sufficient condition to establish the horizon conjecture will be identified. As a consequence of our analysis, we find a no-go theorem for AdS2 backgrounds in heterotic theory. The bulk extension of a prescribed near-horizon geometry will then be considered in various theories. The horizon fields will be expanded at first order in the radial coordinate. The moduli space of radial deformations will be proved to be finite dimensional, by showing that the moduli must satisfy elliptic PDEs. In the second part, geometric aspects and spectral properties of integrable anti-de Sitter backgrounds will be discussed. We formulate a Bethe ansatz in AdS2 x S2 x T6 type IIB superstring, overcoming the problem of the lack of pseudo-vacuum state affecting this background. In AdS3 x S3 x T4 type IIB superstring, we show that the S-matrix is annihilated by the boost generator of the q-deformed Poincaré superalgebra, and interpret this condition as a parallel equation for the S-matrix with respect to a connection on a fibre bundle. This hints that the algebraic problem associated with the scattering process can be geometrically rewritten. This allows us to propose a Universal S-matrix.

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arXiv2017

Massless $AdS_2$ scattering and Bethe ansatz

We first analyse the integrable scattering theory describing the massless excitations of $AdS_2 \times S^2 \times T^6$ superstrings in the relativistic limit. The matrix part of the S-matrix is obtained in the BMN limit from the conjectured exact expression, and compared with known S-matrices with N=1 supersymmetry. A dressing factor, yet unknown for the complete theory, is here constructed based on relativistic crossing symmetry. We derive a Bethe-ansatz condition by employing a transfer-matrix technique based on the so-called free-fermion condition. This is known to overcome the problem of lack of a reference state. We then generalise the method to the massless non-relativistic case, and compare the resulting Bethe-ansatz condition with a simple massless limit of the one conjectured by Sorokin, Tseytlin, Wulff and Zarembo.

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arXiv2016

Massless sector of AdS_3 superstrings: a geometric interpretation

We study the recently discovered q-deformed Poincare' supersymmetry of the AdS_3/CFT_2 integrable massless scattering, and demonstrate how the S-matrix is invariant under boosts. The boost generator has a non-local coproduct, which acts on the scattering matrix as a differential operator, annihilating it. We propose to reinterpret the boost action in terms of covariant derivatives on bundles, and derive an expression for the S-matrix as the path-ordered exponential of a flat connection. We provide a list of possible alternative interpretations of this emergent geometric picture, including a one-dimensional auxiliary Schroedinger problem. We support our claims by performing a simplified algebraic Bethe ansatz, which bears some resemblance to antiferromagnets.

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