arXiv subjects

Andrea Cavaglià

Publications and source records attributed to Andrea Cavaglià.

25 records · Page 2Linked to original sources

arXiv2016

$T \bar{T}$-deformed 2D Quantum Field Theories

It was noticed many years ago, in the framework of massless RG flows, that the irrelevant composite operator $T \bar{T}$, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum field theories, and can be regarded as a peculiar kind of integrable perturbation. Novel interesting features of this operator have recently emerged from the study of effective string theory models.In this paper we study further properties of this distinguished perturbation. We discuss how it affects the energy levels and one-point functions of a general 2D QFT in finite volume through a surprising relation with a simple hydrodynamic equation. In the case of the perturbation of CFTs, adapting a result by Lüscher and Weisz we give a compact expression for the partition function on a finite-length cylinder and make a connection with the exact $g$-function method. We argue that, at the classical level, the deformation naturally maps the action of $N$ massless free bosons into the Nambu-Goto action in static gauge, in $N+2$ target space dimensions, and we briefly discuss a possible interpretation of this result in the context of effective string models.

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arXiv2016

On the Exact Interpolating Function in ABJ Theory

Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ_1,λ_2) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ_1,λ_2). We checked our conjecture against various weak coupling expansions, at strong coupling and also demonstrated its invariance under the Seiberg-like duality. This match also gives further support to the integrability of the model. If our conjecture is correct, it extends all the available integrability results in the ABJM model to the ABJ model.

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arXiv2015

12 loops and triple wrapping in ABJM theory from integrability

Adapting a method recently proposed by C. Marboe and D. Volin for ${\cal N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the $sl(2)$-like sector of planar $\mathcal{N}$=6 super-Chern-Simons. The method relies on the Quantum Spectral Curve formulation of the problem and the expansion is written in terms of the interpolating function $h(λ)$, with coefficients expressible as combinations of Euler-Zagier sums with alternating signs. We present explicit results up to 12 loops (six nontrivial orders) for various twist L=1 and L=2 operators, corresponding to triple and double wrapping terms, respectively, which are beyond the reach of the Asymptotic Bethe Ansatz as well as Lüscher's corrections. The algorithm works for generic values of L and S and in principle can be used to compute arbitrary orders of the weak coupling expansion. For the simplest operator with L=1 and spin S=1, the Padé extrapolation of the 12-loop result nicely agrees with the available Thermodynamic Bethe Ansatz data in a relatively wide range of values of the coupling. A Mathematica notebook with a selection of results is attached.

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arXiv2015

A Riemann-Hilbert formulation for the finite temperature Hubbard model

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

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arXiv2014

The Quantum Spectral Curve of the ABJM theory

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in N = 4 SYM are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ-system or Quantum Spectral Curve. In this letter we present the Pμ-system for the spectrum of the ABJM theory. This may be an important step towards the exact determination of the interpolating function h(λ) characterising the integrability of the ABJM model. We also discuss a surprising symmetry between the Pμ-system equations for N = 4 SYM and ABJM.

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arXiv2011

On the $AdS_5/CFT_4$ TBA and its analytic properties

The thermodynamic Bethe Ansatz equations arising in the context of the $AdS_5/CFT_4$ correspondence exhibit an important difference with respect to their analogues in relativistic integrable quantum field theories: their solutions (the Y functions) are not meromorphic functions of the rapidity, but live on a complicated Riemann surface with an infinite number of branch points and therefore enjoy a new kind of extended Y-system. In this paper we review the analytic properties of the TBA solutions, and present new information coming from their numerical study. An identity allowing to simplify the equations and the numerical implementation is presented, together with various plots which highlight the analytic structure of the Y functions.

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arXiv2010

Extended Y-system for the $AdS_5/CFT_4$ correspondence

We study the analytic properties of the $AdS_5/CFT_4$ Y functions. It is shown that the TBA equations, including the dressing factor, can be obtained from the Y-system with some additional information on the square-root discontinuities across semi-infinite segments in the complex plane. The Y-system extended by the discontinuity relations constitutes a fundamental set of local functional constraints that can be easily transformed into integral form through Cauchy's theorem.

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