arXiv subjects

G. M. Sotkov

Publications and source records attributed to G. M. Sotkov.

At least 19 recordsLinked to original sources

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↗

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

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.

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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.

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arXiv2016

Scale Factor Duality for Conformal Cyclic Cosmologies

The scale factor duality is a symmetry of dilaton gravity which is known to lead to pre-big-bang cosmologies. A conformal time version of the scale factor duality (SFD) was recently implemented as a UV/IR symmetry between decelerated and accelerated phases of the post-big-bang evolution within Einstein gravity coupled to a scalar field. The problem investigated in the present paper concerns the employment of the conformal time SFD methods to the construction of pre-big-bang and cyclic extensions of these models. We demonstrate that each big-bang model gives rise to two qualitatively different pre-big-bang evolutions: a contraction/expansion SFD model and Penrose's Conformal Cyclic Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving certain gauged Kähler sigma models minimally coupled to Einstein gravity are studied. We also describe the specific SFD features of the thermodynamics and the conditions for validity of the generalized second law in the case of Gauss-Bonnet (GB) extension of these selected CCC models.

hep-th↗

arXiv2016

On the thermodynamics of scale factor dual Universes

The thermodynamical aspects of the conformal time scale factor duality (SFD) of cosmological models within Einstein Gravity are investigated. We derive the SFD transformations of the thermodynamical quantities describing the thermal evolution of the matter fluid and of the apparent horizon. The thermodynamical properties of the self-dual cosmological models with a modified Chaplygin gas are studied in detail. We deduce the restrictions on the equation of state parameters that allow to extend scale factor duality as a UV/IR symmetry of the cosmological models consistent with their thermodynamical behavior.

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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↗

arXiv2013

New Massive Gravity Holography

We investigate the holographic renormalization group flows and the classical phase transitions that occur in two dimensional QFT model dual to the New Massive 3D Gravity coupled to scalar matter. Specific matter self-interactions generated by quadratic superpotential are considered. The off-critical $AdS_3/CFT_2$ correspondence determines the exact form of the $ QFT_2$ 's $β$ -function and the singular part of the reduced free energy. The corresponding scaling laws and critical exponents characterizing the RG fixed points as well as the values of the mass gaps in the massive phases are obtained.

hep-th↗

arXiv2013

Self-Duality from New Massive Gravity Holography

The holographic renormalization group (RG) flows in certain self-dual two dimensional QFT's models are studied. They are constructed as holographic duals to specific New Massive 3d Gravity (NMG) models coupled to scalar matter with "partially self-dual" superpotentials. The standard holographic RG constructions allow us to derive the exact form of their $β$- functions in terms of the corresponding NMG's domain walls solutions. By imposing invariance of the free energy, the central function and of the anomalous dimensions under specific matter field's duality transformation, we have found the conditions on the superpotentials of two different NMG's models, such that their dual 2d QFT's are related by a simple strong-weak coupling transformation.

hep-th↗

arXiv2012

Holographic RG Flows from Quasi-Topological Gravity

We investigate the holographic Renormalization Group (RG) flows and the critical phenomena that take place in the $QFT$'s dual to the d-dimensional cubic Quasi-Topological Gravity coupled to scalar matter. The knowledge of the corresponding flat Domain Walls(DWs) solutions, allows us to derive the explicit form of the $QFT$'s beta-functions as well as of the trace anomalies $a(l)$ and $c(l)$-functions in terms of the matter superpotential. As a consequence we are able to determine the complete set of $CFT$ data characterizing the universality classes of the UV and IR critical points and to follow the particular RG evolution of this data. We further analyse the dependence of the critical properties of such dual $QFT$'s on the values of the Lovelock couplings and on the shape of the superpotential. For odd values of $d$, the explicit form of the "a- and c- central charges" as functions of the running coupling constant, enable us to establish the conditions under which the $a/c$-Theorems for their decreasing are valid. The restrictions imposed on the massless Holographic RG flows by the requirements of the positivity of the energy fluxes are derived. The particular case of quartic Higgs-like superpotential is studied in detail. It provides an example of unitary dual $QFT$'s having few $c\ne a$ critical points representing second or infinite order phase transitions. Depending on the range of the values of the coupling constant they exhibit massive and massless phases, described by a chain of distinct DWs solutions sharing common boundaries.

hep-th↗

arXiv2012

Domain Walls in Extended Lovelock Gravity

We derive a BPS-like first order system of equations for a family of flat static domain walls (DWs) of dimensionally extended cubic Lovelock Gravity coupled to massive scalar self-interacting matter. The explicit construction of such DWs is achieved by introducing of an appropriate matter superpotential. We further analyse the dependence of the geometric properties of the asymptotically AdSd space-times representing distinct DWs on the shape of the matter potential, on the values of the Lovelock couplings and on the scalar field boundary conditions. Few explicit examples of Lovelock DWs interpolating between AdS-type vacua of different cosmological constants are presented. In five dimensions our method provides interesting solutions of the Myers-Robinson Quasi-topological Gravity in the presence of matter important for the description of the specific renormalization group flows in its holographic dual four-dimensional CFT perturbed by relevant operators.

hep-th↗

arXiv2010

New Massive Gravity Domain Walls

The properties of the asymptotic $AdS_3$ space-times representing flat domain walls (DW's) solutions of the New Massive 3D Gravity with scalar matter are studied. Our analysis is based on $I^{st}$ order BPS-like equations involving an appropriate superpotential. The Brown-York boundary stress-tensor is used for the calculation of DW's tensions as well as of the $CFT_2$'s central charges. The holographic renormalization group flows and the phase transitions in specific deformed $CFT_2$ dual to 3D massive gravity model with quadratic superpotential are discussed.

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