arXiv subjects

A. A. Lima

Publications and source records attributed to A. A. Lima.

9 recordsLinked to original sources

arXiv2021

Dynamics of R-neutral Ramond fields in the D1-D5 SCFT

We describe the effect of the marginal deformation of the $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-$N$ approximation. Our analysis of their dynamics explores the explicit analytic form of the genus-zero four-point function involving two R-neutral Ramond fields and two deformation operators. We compute this correlation function with two different approaches: the Lunin-Mathur path-integral technique and the stress-tensor method. From its short distance limits, we extract the OPE structure constants and the scaling dimensions of non-BPS fields appearing in the fusion. In the deformed CFT, at second order in the deformation parameter, the two-point function of the $n$-twisted Ramond fields is UV-divergent. We perform an appropriate regularization, together with a renormalization of the undeformed fields, obtaining finite, well-defined corrections to their two-point functions and their bare conformal weights, for $n < N$. The fields with maximal twist $n=N$ remain protected from renormalization, with vanishing anomalous dimensions.

hep-th↗

arXiv2021

On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT

We examine the behavior of the Ramond ground states in the D1-D5 CFT after a deformation of the free-orbifold sigma model on target space $({\mathbb T}^4)^N / S_N$ by a marginal interaction operator. These states are compositions of Ramond ground states of the twisted and untwisted sectors. They are characterized by a conjugacy class of $S_N$ and by the set of their "spins", including both R-charge and "internal" SU(2) charge. We compute the four-point functions of an arbitrary Ramond ground state with its conjugate and two interaction operators, for genus-zero covering surfaces representing the leading orders in the large-$N$ expansion. We examine short distance limits of these four-point functions, shedding light on the dynamics of the interacting theory. We find the OPEs and a collection of structure constants of the ground states with the interaction operators and a set of resulting non-BPS twisted operators. We also calculate the integrals of the four-point functions over the positions of the interaction operators and show that they vanish. This provides an explicit demonstration that the Ramond ground states remain protected against deformations away of the free orbifold point, as expected from algebraic considerations using the spectral flow of the ${\mathcal N} = (4,4)$ superconformal algebra with central charge $c = 6N$.

hep-th↗

arXiv2021

Renormalization of Twisted Ramond Fields in D1-D5 SCFT$_2$

We explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-$N$ limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-$N$ limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.

hep-th↗

arXiv2020

Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT$_2$

We study two families of composite twisted Ramond fields (made by products of two operators) in the $\cal {N}=(4,4)$ supersymmetric D1-D5 SCFT$_2$ deformed by a marginal modulus operator away from its $(T^4)^N/ S_N$ free orbifold point. We construct the large-$N$ contributions to the four-point functions with two composite operators and two deformation fields. These functions allow us to derive short-distance OPE limits and to calculate the anomalous dimensions of the composite operators. We demonstrate that one can distinguish two sets of composite Ramond states with twists $m_1$ and $m_2$: protected states, for which $m_1+m_2=N$, and "lifted" states for which $m_1+m_2<N$. The latter require an appropriate renormalisation. We also derive the leading order corrections to their two-point functions, and to their three-point functions with the deformation operator.

hep-th↗

arXiv2020

Conformal Scale Factor Inversion for Domain Walls and Holography

We describe a correspondence between domain wall solutions of Einstein gravity with a single scalar field and self-interaction potential. The correspondence we call 'conformal scale factor inversion (CSFI)' is a map comprising the inversion of the scale factor in conformal coordinates, and a transformation of the field and its potential which preserves the form of the Einstein equations for static and isotropic domain walls. By construction, CSFI maps the asymptotic AdS boundary to the vicinity of a naked singularity in a theory with a special Liouville (exponential) scalar field potential; it is also a map in the parameter space of exponential potentials. The correspondence can be extended to linear fluctuations, being akin to an S-duality, and can be interpreted in terms of 'SUSY quantum mechanics' for the fluctuation modes. The holographic implementation of CSFI relates the UV and IR regimes of a pair of holographic renormalization group flows; in particular, it is a symmetry of the GPPZ flow.

hep-th↗

arXiv2020

Microstate Renormalization in Deformed D1-D5 SCFT

We derive the corrections to the conformal dimensions of twisted Ramond ground states in the deformed two-dimensional $\mathcal N = (4,4)$ superconformal $(\mathbb T^4)^N/S_N$ orbifold theory describing bound states of the D1-D5 brane system in type IIB superstring theory. Our result holds to second order in the deformation parameter, and at the large $N$ planar limit. The method of calculation involves the analytic evaluation of integrals of four-point functions of two R-charged twisted Ramond fields and two marginal deformation operators. We also calculate the deviation from zero, at first order in the considered marginal perturbation, of the structure constant of the three-point function of two Ramond fields and one deformation operator.

hep-th↗

arXiv2019

SUSY shields the scaling symmetry of conformal quantum mechanics

Renormalization of the inverse square potential usually breaks its classical conformal invariance. In a strongly attractive potential, the scaling symmetry is broken to a discrete subgroup while, in a strongly repulsive potential, it is preserved at quantum level. In the intermediate, weak-medium range of the coupling, an anomalous length scale appears due to a flow of the renormalization group away from a critical point. We show that potentials with couplings in the strongly-repulsive and in the weak-medium ranges can be related by a dynamical supersymmetry. Imposing SUSY invariance unifies these two ranges, and fixes the anomalous scale to zero, thus restoring the continuous scaling symmetry.

hep-th↗

arXiv2015

Scale Factor Self-Dual Cosmological Models

We implement a conformal time scale factor duality for Friedmann-Robertson-Walker cosmological models, which is consistent with the weak energy condition. The requirement for self-duality determines the equations of state for a broad class of barotropic fluids. We study the example of a universe filled with two interacting fluids, presenting an accelerated and a decelerated period, with manifest UV/IR duality. The associated self-dual scalar field interaction turns out to coincide with the "radiation-like" modified Chaplygin gas models. We present an equivalent realization of them as gauged Kähler sigma models (minimally coupled to gravity) with very specific and interrelated Kähler- and super-potentials. Their applications in the description of hilltop inflation and also as quintessence models for the late universe are discussed.

hep-th↗

arXiv2013

Energy Density Bounds in Cubic Quasi-Topological Cosmology

We investigate the thermodynamical and causal consistency of cosmological models of the cubic Quasi-Topological Gravity (QTG) in four dimensions, as well as their phenomenological consequences. Specific restrictions on the maximal values of the matter densities are derived by requiring the apparent horizon's entropy to be a non-negative, non-decreasing function of time. The QTG counterpart of the Einstein-Hilbert (EH) gravity model of linear equation of state is studied in detail. An important feature of this particular QTG cosmological model is the new early-time acceleration period of the evolution of the Universe, together with the standard late-time acceleration present in the original EH model. The QTG correction to the causal diamond's volume is also calculated.

gr-qc↗