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Matteo Beccaria

Publications and source records attributed to Matteo Beccaria.

At least 91 records · Page 5Linked to original sources
arXiv2012

A staggered fermion chain with supersymmetry on open intervals

A strongly-interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the ground states as a function of the staggering parameter are examined. In particular, a connection between certain ground-state components and solutions of non-linear recursion relations associated with the Painlevé VI equation is conjectured. Moreover, various local occupation probabilities in the ground state have the so-called scale-free property, and allow for an exact resummation in the limit of infinite system size.

cond-mat.stat-mech↗
arXiv2012

More about "short" spinning quantum strings

We continue investigation of the spectrum of semiclassical quantum strings in AdS5 x S5 on the examples of folded (S,J) string (with spin S in AdS5 and orbital momentum J in S5) dual to an sl(2) sector state in gauge theory and its (J',J) counterpart with spin J' in S5 dual to an su(2) sector state. We study the limits of small spins and large J at weak and strong coupling, pointing out that terms linear in spins provide a generalization of "protected" coefficients in the energy that are given by finite polynomials in 't Hooft coupling λ (or square of string tension) for any value of λ. We propose an expression for the coefficient of the term linear in spin J' in the (J',J) string energy which should be the su(2) sector counterpart of the "slope function" in the sl(2) sector suggested by Basso in arXiv:1109.3154.

hep-th↗
arXiv2012

Wrapping corrections beyond the sl(2) sector in N=4 SYM

The sl(2) sector of N=4 SYM theory has been much studied and the anomalous dimensions of those operators are well known. Nevertheless, many interesting operators are not included in this sector. We consider a class of twist operators beyond the sl(2) subsector introduced by Freyhult, Rej and Zieme. They are spin n, length-3 operators. At one-loop they can be identified with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS_5 space and charge in S^5. We exploit the Y-system to compute the leading weak-coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin n. We combine the wrapping correction with the known four loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin n. In particular, at large n, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL-like equation predicting the rightmost leading poles.

hep-th↗
arXiv2012

Leading quantum correction to energy of "short" spiky strings

We consider semiclassical quantization of spiky strings spinning in AdS_3 part of AdS_5 X S^5 using integrability-based (algebraic curve) method. In the "short string" (small spin) limit the expansion of string energy starts with its flat-space expression. We compute the leading quantum string correction to "short" spiky string energy and find the explicit form of the corresponding 1-loop coefficient a_01. It turns out to be rational and expressed in terms of the harmonic sums as functions of the number n of spikes. In the special case of n=2 when the spiky string reduces to the single-folded spinning string the coefficient a_01 takes the value (-1/4) found in arXiv:1102.1040. We also consider a similar computation for the m-folded string and more general spiky string with an extra "winding" number, finding similar expressions for a_01. These results may be useful for a description of energies of higher excited states in the quantum AdS_5 X S^5 string spectrum, generalizing earlier discussions of the string counterparts of the Konishi operator.

hep-th↗
arXiv2012

Resummation of semiclassical short folded string

We reconsider semiclassical quantization of folded string spinning in AdS_3 part of AdS_5 X S^5 using integrability-based (algebraic curve) method. We focus on the "short string" (small spin S) limit with the angular momentum J in S^5 scaled down according to \cal J = rho \sqrt \cal S in terms of the variables \cal J = J/\sqrtλ, \cal S = S/\sqrtλ. The semiclassical string energy in this particular scaling limit admits the double expansion E = \sum_{n=0}^{\infty}\sum_{p=0}^{\infty} (\sqrtλ)^{1-n}\,a_{n,p}(rho)\, \cal S^{p+1/2}. It behaves smoothly as J -> 0 and partially resums recent results by Gromov and Valatka. We explicitly compute various one-loop coefficients a_{1,p}(rho) by summing over the fluctuation frequencies for integrable perturbations around the classical solution. For the simple folded string, the result agrees with what could be derived exploiting a recent conjecture of Basso. However, the method can be extended to more general situations. As an example, we consider the m-folded string where Basso's conjecture fails. For this classical solution, we present the exact values of a_{1,0}(rho) and a_{1,1}(rho) for m=2, 3, 4, 5 and explain how to work out the general case.

hep-th↗
arXiv2011

Quantum folded string in S^5 and the Konishi multiplet at strong coupling

The Konishi superconformal multiplet is an important theoretical laboratory where one can test AdS/CFT methods to compute strong coupling corrections to the spectrum of superstrings in AdS_5 x S^5. In particular, one can exploit integrability for finite charge states/operators. The multiplet ground state is a singlet operator with two simple descendants in the rank-1 sectors sl(2) and su(2) of N=4 super Yang-Mills theory. Recently, the next-to-leading quantum correction to the sl(2) state has been computed. Here, we use the algebraic curve approach to determine the correction to the other state recovering universality of the correction inside the multiplet.

hep-th↗
arXiv2011

Large spin expansion of the wrapping correction to Freyhult-Rej-Zieme twist operators

Twist operators in the closed sl(2) sector of planar N=4 SYM are characterized by their spin. The explicit dependence of anomalous dimensions on this important parameter is a source of interesting information. Wrapping corrections are a non trivial part of the calculation and are under control in the framework of thermodynamical Bethe Ansatz valid for the full theory and thoroughly checked in that sector. The extension to more general twist operators beyond sl(2) has been recently accomplished for the so-called 3-gluon operators that are a special case of the generalized twist operators introduced by Freyhult, Rej and Zieme. Such operators are dual to spinning strings configurations with two spins S1, S2 in AdS_5 and charge in S^5. We compute the expansion of the weak-coupling leading order wrapping correction in the gauge theory limit dual to large S1 and fixed S2. We present a simple algorithm for the calculation and provide explicit results illustrating the general structure of the expansion.

hep-th↗
arXiv2011

Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM

We consider N=4 SYM and a class of spin N, length-3, twist operators beyond the well studied sl(2) subsector. They can be identified at one-loop with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS5. We exploit the Y-system to compute the leading weak-coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin N. We combine the wrapping correction with the known four-loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin N. In particular, at large N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL-like equation predicting the rightmost leading poles.

hep-th↗
arXiv2011

Y-system for Z_S Orbifolds of N=4 SYM

We propose a twisted Y-system for the calculation of leading wrapping corrections to physical states of general Z_S orbifold projections of N=4 super Yang-Mills theory. Agreement with available thermodynamical Bethe Ansatz results is achieved in the non supersymmetric case. Various examples of new computations, including other supersymmetric orbifolds are illustrated.

hep-th↗
arXiv2011

On wrapping corrections to GKP-like operators

In the recent paper arXiv:1010.5009, Maldacena et al. derive the two loop expressions for polygonal Wilson loops expectation values, or MHV amplitudes, by writing them as sums over exchanges of intermediate free particles. The spectrum of excitations of the flux tube between two null Wilson lines can be viewed as the spectrum of excitations around the infinite spin limit of finite twist operators in the sl(2) sector of N=4 SYM or the Gubser-Klebanov-Polyakov (GKP) string. This regime can be captured exploiting integrability and assuming that wrapping corrections are negligible compared to asymptotic Bethe Ansatz contributions. This assumption holds true for the N=4 SYM background GKP string, but deserves further analysis for excited states. Here, we investigate GKP cousins by considering various classes of (generalized) twist operators in beta-deformed N=4 SYM and ABJM theory. We show that the Y-system of Gromov-Kazakov-Vieira easily leads to accurate large spin expansions of the wrapping correction at lowest order in weak-coupling perturbation theory. As a byproduct, we confirm that wrapping corrections are subleading in all the considered cases.

hep-th↗
arXiv2010

Counting charged massless states in the (0,2) heterotic CFT/geometry connection

We use simple current techniques and their relation to orbifolds with discrete torsion for studying the (0,2) CFT/geometry duality with non-rational internal N=2 SCFTs. Explicit formulas for the charged spectra of heterotic SO(10) GUT models are computed in terms of their extended Poincaré polynomials and the complementary Poincaré polynomial which can be computed in terms of the elliptic genera. While non-BPS states contribute to the charged spectrum, their contributions can be determined also for non-rational cases. For model building, with generalizations to SU(5) and SM gauge groups, one can take advantage of the large class of Landau-Ginzburg orbifold examples.

hep-th↗
arXiv2010

Semiclassical short strings in AdS_5 x S^5

We present results for the one-loop correction to the energy of a class of string solutions in AdS_5 x S^5 in the short string limit. The computation is based on the observation that, as for rigid spinning string elliptic solutions, the fluctuation operators can be put into the single-gap Lame' form. Our computation reveals a remarkable universality of the form of the energy of short semiclassical strings. This may help to understand better the structure of the strong coupling expansion of the anomalous dimensions of dual gauge theory operators.

hep-th↗
arXiv2010

A numerical test of the Y-system in the small size limit of the SU(2)x SU(2) Principal Chiral Model

Recently, Kazakov, Gromov and Vieira applied the discrete Hirota dynamics to study the finite size spectra of integrable two dimensional quantum field theories. The method has been tested from large values of the size L down to moderate values using the SU(2) x SU(2) principal chiral model as a theoretical laboratory. We continue the numerical analysis of the proposed non-linear integral equations showing that the deep ultraviolet region L -> 0 is numerically accessible. To this aim, we introduce a relaxed iterative algorithm for the numerical computation of the low-lying part of the spectrum in the U(1) sector. We discuss in details the systematic errors involved in the computation. When a comparison is possible, full agreement is found with previous TBA computations.

hep-th↗
arXiv2009

Reciprocity and integrability in the sl(2) sector of N=4 SYM

We analyze the higher conserved charges of type IIB superstring on AdS5 x S5 from the perspective of a recently discovered generalized Gribov-Lipatov reciprocity. We provide several evidences that reciprocity holds for all the higher charges and not only for the energy. This is discussed in the simple case of twist L=2, and 3 operators in the sl(2) subsector at (a) multi-loop level in weak coupling, (b) classical level at strong coupling for the dual folded string.

hep-th↗
arXiv2009

The virtual scaling function of twist operators in the N=6 Chern-Simons theory

We consider twist-L operators in the planar N=6 superconformal Chern-Simons ABJM theory. Their anomalous dimension gamma_L^{CS}(N) is a function of the twist L, the spin N, and the dressed coupling of ABJM. We show that at next-to-leading order in the large spin expansion, this anomalous dimension is related to that of N=4 SYM twist operators by a simple scaling law.

hep-th↗
arXiv2009

QCD properties of twist operators in the N=6 Chern-Simons theory

We consider twist-1, 2 operators in planar N=6 superconformal Chern-Simons ABJM theory. We derive higher order anomalous dimensions from integrability and test various QCD-inspired predictions known to hold in N=4 SYM. In particular, we show that the asymptotic anomalous dimensions display intriguing remnants of Gribov-Lipatov reciprocity and Low-Burnett-Kroll logarithmic cancellations. Wrapping effects are also discussed and shown to be subleading at large spin.

hep-th↗
arXiv2009

On the wrapping correction to single magnon energy in twisted N=4 SYM

We apply Zeilberger summation to derive a closed formula for the wrapping correction to one-impurity states in the su(2) sector of the beta-deformed N=4 SYM theory at beta=1/2. As an application depending heavily on the result, we compute the large volume expansion of the wrapping correction.

hep-th↗