Scalar Deformations Research Articles

Imprints of phase transitions on Kasner singularities

Under the AdS/CFT correspondence, asymptotically anti–de Sitter geometries with backreaction can be viewed as conformal field theory states subject to a renormalization group (RG) flow from an ultraviolet (UV) description toward an infrared (IR) sector. For black holes, however, the IR point is the horizon, so one way to interpret the interior is as an analytic continuation to a “trans-IR” imaginary-energy regime. In this paper, we demonstrate that this analytic continuation preserves some imprints of the UV physics, particularly near its “end point” at the classical singularity. We focus on holographic phase transitions of geometric objects in round black holes. We first assert the consistency of interpreting such black holes, including their interiors, as RG flows by constructing a monotonic a function. We then explore how UV phase transitions of entanglement entropy and scalar two-point functions, each of which are encoded by bulk geometry under the holographic mapping, are related to the structure of the near-singularity geometry, which is quantified by Kasner exponents. Using 2D holographic flows triggered by relevant scalar deformations as test beds, we find that the 3D bulk’s near-singularity Kasner exponents can be viewed as functions of the UV physics precisely when the deformation is nonzero. Published by the American Physical Society 2024

Consistent truncations from the geometry of sphere bundles

In this paper, we present a unified perspective on sphere consistent truncations based on the classical geometric properties of sphere bundles. The backbone of our approach is the global angular form for the sphere. A universal formula for the Kaluza-Klein ansatz of the flux threading the n-sphere captures the full nonabelian isometry group SO(n + 1) and scalar deformations associated to the coset SL(n + 1, ℝ)/SO(n + 1). In all cases, the scalars enter the ansatz in a shift by an exact form. We find that the latter can be completely fixed by imposing mild conditions, motivated by supersymmetry, on the scalar potential arising from dimensional reduction of the higher dimensional theory. We comment on the role of the global angular form in the derivation of the topological couplings of the lower-dimensional theory, and on how this perspective could provide inroads into the study of consistent truncations with less supersymmetry.

Scalar curvature and deformations of complex structures

Abstract We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kähler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an infinite-dimensional Kähler reduction, which is a hyperkähler reduction for a particular choice of the spectral function. The main tool for studying the system is a flat connection on the space of first-order deformations of the complex structure, that allows to obtain a formal complexification of the moment map equations. Using this connection, we describe a variational characterization of the equations, a Futaki invariant for the system, and a generalization of K-stability that is conjectured to characterize the existence of solutions.

Exceptional Algebroids and Type IIA Superstrings

AbstractWe study exceptional algebroids in the context of warped compactifications of type IIA string theory down to n dimensions, with . In contrast to the M‐theory and type IIB case, the relevant algebroids are no longer exact, and their locali moduli space is no longer trivial, but has 5 distinct points. This relates to two possible scalar deformations of the IIA theory. The proof of the local classification shows that, in addition to these scalar deformations, one can twist the bracket using a pair of 1‐forms, a 2‐form, a 3‐form, and a 4‐form. Furthermore, we use the analysis to translate the classification of Leibniz parallelisable spaces (corresponding to maximally supersymmetric consistent truncations) into a tractable algebraic problem. We finish with a discussion of the Poisson–Lie U‐duality and examples given by tori and spheres in 2, 3, and 4 dimensions.

Geometry for a Symmetrıc 2-Path Atom Interferometer Model

It is often argued that the sensitivity of atom interferometer depends on the geometry of the interfering atom paths, conventionally, atom interferometer are usually configured to be sensitive to all deformations including tensor and scalar field deformations, it is a promising and robust tool for obtaining a highly sensitive and accurate measurements of gravitational signals, as such they are potentially capable of testing a wide range of fundamental physics questions including gravitational decoherence. Therefore, motivated by the recent search to improve the sensitivity of the next generation atom interferometer, we derived a broad class of equations that obeys a specific geometric configuration for the interfering paths for a 2-level atom interferometer model, and in doing so, we further analysed various configurations for the geometric interpretation, in addition to interferometric influence phase shift and a possible decoherence factor which could lead to a systematic theoretical framework for future sensing of weak forces, due to, for example, gravitational waves and light dark matter.

4-point function from conformally coupled scalar in AdS6

We explore conformally coupled scalar theory in AdS6 extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling λ. We describe how we get the classical solutions by diagrammatic ways which show general rules constructing the classical solutions. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension ∆ = 3, from the classical solutions. We do not assume any specific form of the micro Lagrangian density of the 5-dimensional conformal field theory. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the ∆ = 3 scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect SO(5) rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic n-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of n-point function by connecting l-point functions each other where l < n. In the co-linear limit, these n-point functions reproduce the conformal n-point functions of ∆ = 3 scalar operators in d = 5 Euclidean space addressed in arXiv:2001.05379.

Alternative Lagrangians obtained by scalar deformations

We study mechanical systems that can be recast into the form of a system of genuine Euler–Lagrange equations. The equations of motions of such systems are initially equivalent to the system of Lagrange equations of some Lagrangian [Formula: see text], including a covariant force field. We find necessary and sufficient conditions for the existence of a differentiable function [Formula: see text] such that the initial system is equivalent to the system of Euler–Lagrange equations of the deformed Lagrangian [Formula: see text].

Bounds on the local energy density of holographic CFTs from bulk geometry

The stress tensor is a basic local operator in any field theory; in the context of AdS/CFT, it is the operator which is dual to the bulk geometry itself. Here we exploit this feature by using the bulk geometry to place constraints on the local energy density in static states of holographic (2+1)-dimensional CFTs living on a closed (but otherwise generally curved) spatial geometry. We allow for the presence of a marginal scalar deformation, dual to a massless scalar field in the bulk. For certain vacuum states in which the bulk geometry is well-behaved at zero temperature, we find that the bulk equations of motion imply that the local energy density integrated over specific boundary domains is negative. In the absence of scalar deformations, we use the inverse mean curvature flow to show that if the CFT spatial geometry has spherical topology but non-constant curvature, the local energy density must be positive somewhere. This result extends to other topologies, but only for certain types of vacuum; in particular, for a generic toroidal boundary, the vacuum’s bulk dual must be the zero-temperature limit of a toroidal black hole.

Moduli spaces of AdS5 vacua in N $$ \mathcal{N} $$ = 2 supergravity

We determine the conditions for maximally supersymmetric AdS_5 vacua of five-dimensional gauged N=2 supergravity coupled to vector-, tensor- and hypermultiplets charged under an arbitrary gauge group. In particular, we show that the unbroken gauge group of the AdS_5 vacua has to contain an U(1)_R-factor. Moreover we prove that the scalar deformations which preserve all supercharges form a Kahler submanifold of the ambient quaternionic Kahler manifold spanned by the scalars in the hypermultiplets.

Holography for anisotropic branes with hyperscaling violation

In this paper, based on the principles of Gauge/gavity duality, we explore the field theory description of certain special class of strongly coupled hyperscaling violating QFTs in the presence of scalar deformations near the \textit{effective} dynamical scale ($ r_F $) of the theory. In the language of the AdS/CFT duality, the scalar deformations of the above type could be thought of as being sourced due to some massless scalar excitation in the bulk which explicitly break the $ SO(2) $ rotational invariance along the spatial directions of the brane. As a consequence of these deformations, it turns out that when we probe such QFTs in terms of its non-local observable like, the entanglement entropy as well as the Wilson operator they indeed receive finite contributions near the effective dynamical scale ($ r_F $) of the theory.

Perturbative search for dead-end CFTs

To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as $\mathcal{O}(10^{-5})$ and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.

On the stability of Riemannian manifold with parallel spinors

Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor. We also prove a rigidity result for special holonomy metrics. In the case of SU(m) holonomy, the rigidity result implies that scalar flat deformations of Calabi-Yau metric must be Calabi-Yau. Finally we explore the connection with a positive mass theorem of [D03], which presents another approach to proving these stability and rigidity results.