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Alessandro Torrielli

Publications and source records attributed to Alessandro Torrielli.

At least 55 records · Page 3Linked to original sources
arXiv2014

Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4

We establish features of so-called Yangian secret symmetries for AdS3 type IIB superstring backgrounds thus verifying the persistence of such symmetries to this new instance of the AdS/CFT correspondence. Specifically, we find two a priori different classes of secret symmetry generators. One class of generators, anticipated from the previous literature, is more naturally embedded in the algebra governing the integrable scattering problem. The other class of generators is more elusive, and somewhat closer in its form to its higher-dimensional AdS5 counterpart. All of these symmetries respect left-right crossing. In addition, by considering the interplay between left and right representations, we gain a new perspective on the AdS5 case. We also study the RTT-realisation of the Yangian in AdS3 backgrounds thus establishing a new incarnation of the Beisert-de Leeuw construction.

hep-th↗
arXiv2014

5D partition functions, q-Virasoro systems and integrable spin-chains

We analyze N = 1 theories on S5 and S4 x S1, showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We demonstrate that, when the 5d mass parameters are analytically continued to suitable values, the S5 and S4 x S1 partition functions degenerate to those for S3 and S2 x S1. We explain this mechanism via the recently proposed correspondence between 5d partition functions and correlators with underlying q-Virasoro symmetry. From the q-Virasoro 3-point functions, we axiomatically derive a set of associated reflection coefficients, and show they can be geometrically interpreted in terms of Harish-Chandra c-functions for quantum symmetric spaces. We then link these particular c-functions to the types appearing in the Jost functions encoding the asymptotics of the scattering in integrable spin chains, obtained taking different limits of the XYZ model to XXZ-type.

hep-th↗
arXiv2013

Dressing phases of AdS3/CFT2

We determine the all-loop dressing phases of the AdS3/CFT2 integrable system related to type IIB string theory on AdS3 x S3 x T4 by solving the recently found crossing relations and studying their singularity structure. The two resulting phases present a novel structure with respect to the ones appearing in AdS5/CFT4 and AdS4/CFT3. In the strongly-coupled regime, their leading order reduces to the universal Arutyunov-Frolov-Staudacher phase as expected. We also compute their sub-leading order and compare it with recent one-loop perturbative results, and comment on their weak-coupling expansion.

hep-th↗
arXiv2013

The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector

We bootstrap the all-loop dynamic S-matrix for the homogeneous psu(1,1|2)^2 spin-chain believed to correspond to the discretization of the massive modes of string theory on AdS_3 x S^3 x T^4. The S-matrix is the tensor product of two copies of the su(1|1)^2 invariant S-matrix constructed recently for the d(2,1;alpha)^2 chain, and depends on two antisymmetric dressing phases. We write down the crossing equations that these phases have to satisfy. Furthermore, we present the corresponding Bethe Ansatz, which differs from the one previously conjectured, and discuss how our construction matches several recent perturbative calculations.

hep-th↗
arXiv2013

On the massless modes of the AdS3/CFT2 integrable systems

We make a proposal for incorporating massless modes into the spin-chain of the AdS3/CFT2 integrable system. We do this by considering the alpha to 0 limit of the alternating d(2,1;alpha)^2 spin-chain constructed in arXiv:1106.2558. In the process we encounter integrable spin-chains with non-irreducible representations at some of their sites. We investigate their properties and construct their R-matrices in terms of Yangians.

hep-th↗
arXiv2012

Multi-parametric R-matrix for the sl(2|1) Yangian

We study the Yangian of the sl(2|1) Lie superalgebra in a multi-parametric four-dimensional representation. We use Drinfeld's second realization to independently rederive the R-matrix, and to obtain the antiparticle representation, the crossing and the unitarity condition. We consistently apply the Yangian antipode and its inverse to the individual particles involved in the scattering. We explicitly find a scalar factor solving the crossing and unitarity conditions, and study the analytic structure of the resulting dressed R-matrix. The formulas we obtain bear some similarities with those familiar from the study of integrable structures in the AdS/CFT correspondence, although they present obvious crucial differences.

math-ph↗
arXiv2012

Secret Symmetries in AdS/CFT

We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.

hep-th↗
arXiv2012

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010.

hep-th↗
arXiv2011

The Quantum Affine Origin of the AdS/CFT Secret Symmetry

We find a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain. We show that this symmetry originates from the quantum affine superalgebra U_q(gl(2|2)), and in the rational limit exactly reproduces the secret symmetry of the AdS/CFT worldsheet S-matrix.

hep-th↗
arXiv2011

The Bound State S-Matrix for AdS5 x S5 Superstring

We determine the S-matrix that describes scattering of arbitrary bound states in the light-cone string theory in AdS5 x S5. The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the S-matrix entries turns out to be the hypergeometric function 4F3. We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Luescher approaches to the finite-size spectral problem. They also shed some light on the construction of the universal R-matrix for the centrally-extended psu(2|2) superalgebra.

hep-th↗
arXiv2011

Yangians, S-matrices and AdS/CFT

This review is meant to be an account of the properties of the infinite-dimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected in a five-year span of research on the subject. We hope this exercise will be useful for future attempts to study Yangians in field and string theories, with or without supersymmetry.

hep-th↗
arXiv2010

Open string pair creation from worldsheet instantons

Worldline instantons provide a particularly elegant way to derive Schwinger's well-known formula for the pair creation rate due to a constant electric field in quantum electrodynamics. In this note, we show how to extend this method to the corresponding problem of open string pair creation.

hep-th↗
arXiv2010

On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra

The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the light-cone string sigma model on AdS5 x S5. We consider an evaluation representation of the conventional Yangian built over a particular 16-dimensional long representation of the centrally extended su(2|2). Interestingly, we find that S-matrices compatible with this evaluation representation do not exist. On the other hand, by requiring centrally extended su(2|2) invariance and explicitly solving the Yang-Baxter equation, we find a scattering matrix for long-short representations of the Lie superalgebra. We notice that this S-matrix is invariant under a different representation of non-evaluation type, induced from the tensor product of short representations. Our findings concern the conventional Yangian only, and are not applied to possible algebraic extensions of the latter.

hep-th↗
arXiv2009

Bound State Transfer Matrix for AdS5 x S5 Superstring

We apply the algebraic Bethe ansatz technique to compute the eigenvalues of the transfer matrix constructed from the general bound state S-matrix of the light-cone AdS5 x S5 superstring. This allows us to verify certain conjectures on the quantum characteristic function, and to extend them to the general case.

hep-th↗
arXiv2009

Universal blocks of the AdS/CFT Scattering Matrix

We identify certain blocks in the S-matrix describing the scattering of bound states of the AdS5 x S5 superstring that allow for a representation in terms of universal R-matrices of Yangian doubles. For these cases, we use the formulas for Drinfeld's second realization of the Yangian in arbitrary bound-state representations to obtain the explicit expressions for the corresponding R-matrices. We then show that these expressions perfectly match with the previously obtained S-matrix blocks.

hep-th↗
arXiv2008

Structure of the string R-matrix

By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R-matrix, in a form that carries explicit dependence on the representation labels, the braiding factors, and the spectral parameters u_i. In this way, we demonstrate that there exist a rewriting of its entries, such that the dependence on the spectral parameters is purely of difference form. Namely, the latter enter only in the combination u_1-u_2, as indicated by the shift automorphism of the Yangian. When recasted in this fashion, the entries exhibit a cleaner structure, which allows to spot new interesting relations among them. This permits to package them into a practical tensorial expression, where the non-diagonal entries are taken care by explicit combinations of symmetry algebra generators.

hep-th↗
arXiv2008

On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian

We construct Drinfeld's second realization of the Yangian based on psu(2|2)xR^3 symmetry. The second realization is traditionally more suitable for deriving the quantum double and the universal R matrix with respect to the first realization, originally obtained by Beisert, and it is generically more useful in order to study finite dimensional representations. We show that the two realization are isomorphic, where the isomorphism is almost the standard one given by Drinfeld for simple Lie algebras, but needs some crucial corrections to account for the central charges. We also evaluate the generators of the second realization on the fundamental representation, finding the interesting result that the rapidity variable for some generators gets boosted by the energy eigenvalue.

hep-th↗