arXiv subjects

Andre Alves Lima

Publications and source records attributed to Andre Alves Lima.

5 recordsLinked to original sources

arXiv2026

Exact solution of the Seven-Vertex Model on a dynamical lattice

We give the complete solution of the one-parameter deformation of the six-vertex model on dynamical lattice introduced in [1] and dubbed gravitational seven-vertex model. The statistical model in question is mapped to a gas of self- and mutually avoiding loops on dynamical triangulations, with a temperature coupling controlling the volume not occupied by loops. The phase diagram is characterised by massive, dilute and dense critical phases, similarly to the gravitational O(n) loop model. There is however an important difference -- in our model the weights of the loops are not topological but depend on the form of the loop and on the curvature defects of the lattice via lattice spin connection. The seven-vertex model on dynamical lattice is nevertheless exactly solvable after being reformulated as a large-N matrix model, which we will refer to as 7vMM, and the solution in the scaling limit was found in [1]. Here we derive the full solution in terms of Jacobi theta functions and present the (non-algebraic) spectral curve of 7vMM in a parametric form. We obtain the phase diagram in the space of the two coupling constants -- the cosmological constant and the temperature -- and identify the critical phases along the boundary of the physical domain. We derive the scaling solution of [1] as the asymptotic of the full solution in the vicinity of the tricritical point separating the phases of dense and massive loops.

hep-th↗

arXiv2026

Four-point functions with fractional R-symmetry excitations in the D1-D5 CFT

We study correlation functions with fractional-mode excitations of the R-symmetry currents in D1-D5 CFT. We show how fractional-mode excitations lift to the covering surface associated with correlation functions as a specific sum of integer-mode excitations, with coefficients that can be determined exactly from the covering map in terms of Bell polynomials. We consider the four-point functions of fractional excitations of two chiral/anti-chiral NS fields, Ramond ground states and the twist-two scalar modulus deformation operator that drives the CFT away from the free point. We derive explicit formulas for classes of these functions with twist structures $(n)$-$(2)$-$(2)$-$(n)$ and $(n_1)(n_2)$-$(2)$-$(2)$-$(n_1)(n_2)$, the latter involving double-cycle fields. The final answer for the four-point functions always depends only on the lift of the base-space cross-ratio. We discuss how this relates to Hurwitz blocks associated with different conjugacy classes of permutations, the corresponding OPE channels and fusion rules.

hep-th↗

arXiv2023

Renormalization group and spectra of the generalized Pöschl-Teller potential

We study the Pöschl-Teller potential $V(x) = α^2 g_s \sinh^{-2}(αx) + α^2 g_c \cosh^{-2}(αx)$, for every value of the dimensionless parameters $g_s$ and $g_c$, including the less usual ranges for which the regular singularity at the origin prevents the Hamiltonian from being self-adjoint. We apply a renormalization procedure to obtain a family of well-defined energy eigenfunctions, and study the associated renormalization group (RG) flow. We find an anomalous length scale that appears by dimensional transmutation, and spontaneously breaks the asymptotic conformal symmetry near the singularity, which is also explicitly broken by the dimensionful parameter $α$ in the potential. These two competing ways of breaking conformal symmetry give the RG flow a rich structure, with phenomena such as a possible region of walking coupling, massive phases, and non-trivial limits even when the anomalous dimension is absent. We show that supersymmetry of the potential, when present, is also spontaneously broken, along with asymptotic conformal symmetry. We use the family of eigenfunctions to compute the S-matrix in all regions of parameter space, for any value of anomalous scale, and systematically study the poles of the S-matrix to classify all bound, anti-bound and metastable states, including quasi-normal modes. The anomalous scale, as expected, changes the spectra in non-trivial ways.

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arXiv2022

Four-point functions with multi-cycle fields in symmetric orbifolds and the D1-D5 CFT

We study $S_N$-invariant four-point functions with two generic multi-cycle fields and two twist-2 fields, at the free orbifold point of the D1-D5 CFT. We derive the explicit factorization of these functions following from the action of the symmetric group on the composite multi-cycle fields. Apart from non-trivial symmetry factors that we compute, the function with multi-cycle operators is reduced to a sum of connected correlators in which the composite fields have, at most, two cycles. The correlators with two double-cycle and two single-cycle fields give the leading order contribution in the large-$N$ limit. We derive explicit formulas for these functions, encompassing a large class of choices for the single- and the double-cycle fields, including generic Ramond ground states, NS chiral fields and the marginal deformation operator. We are thus able to extract important dynamical information from the short-distance OPEs: conformal dimensions, R-charges and structure constants of families of BPS and non-BPS fields present in the corresponding light-light and heavy-light channels. We also discuss properties of generic multi-cycle $Q$-point functions in $M^N/S_N$ orbifolds, using a technology due to Pakman, Rastelli and Razamat.

hep-th↗

arXiv2021

Ramond States of the D1-D5 CFT away from the free orbifold point

The free orbifold point of the D1-D5 CFT must be deformed with a scalar marginal operator driving it to the region in moduli space where the holographic supergravity description of fuzzball microstates becomes available. We discuss the effects of the deformation operator on the twisted Ramond ground states of the CFT by computing four-point functions. One can thus extract the OPEs of the deformation operator with these Ramond fields to find the conformal dimensions of intermediate non-BPS states and the relevant structure constants. We also compute the anomalous dimensions at second order in perturbation theory, and find that individual single-cycle Ramond fields are renormalized, while the full multi-cycle ground states of the $S_N$ orbifold remain protected at leading order in the large-$N$ expansion.

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