Higher-dimensional Theories Research Articles

Slowly rotating black holes in quasitopological gravity

While cubic Quasi-topological gravity is unique, there is a family of quartic Quasi-topological gravities in five dimensions. These theories are defined by leading to a first order equation on spherically symmetric spacetimes, resembling the structure of the equations of Lovelock theories in higher-dimensions, and are also ghost free around AdS. Here we construct slowly rotating black holes in these theories, and show that the equations for the off-diagonal components of the metric in the cubic theory are automatically of second order, while imposing this as a restriction on the quartic theories allows to partially remove the degeneracy of these theories, leading to a three-parameter family of Lagrangians of order four in the Riemann tensor. This shows that the parallel with Lovelock theory observed on spherical symmetry, extends to the realm of slowly rotating solutions. In the quartic case, the equations for the slowly rotating black hole are obtained from a consistent, reduced action principle. These functions admit a simple integration in terms of quadratures. Finally, in order to go beyond the slowly rotating regime, we explore the consistency of the Kerr-Schild ansatz in cubic Quasi-topological gravity. Requiring the spacetime to asymptotically match with the rotating black hole in GR, for equal oblateness parameters, the Kerr-Schild deformation of an AdS vacuum, does not lead to a solution for generic values of the coupling. This result suggests that in order to have solutions with finite rotation in Quasi-topological gravity, one must go beyond the Kerr-Schild ansatz.

Area law of connected correlation function in higher dimensional conformal field theory

We present a new area law which is associated with the correlator of OPE blocks in higher dimensional conformal field theories (CFTs). The area law shows similar behaviour as black hole entropy or geometric entanglement entropy. It includes a leading term which is proportional to the area of the entanglement surface, and a logarithmic subleading term with degree q. We extract the UV cutoff independent coefficients and discuss various properties of the coefficients.

Emergent gravity from hidden sectors and TT deformations

We investigate emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor. We derive the general effective description of such dynamics, and apply it to the case where a hidden theory generates gravity that is coupled to the Standard Model. In the linearized description, generically, such gravity is massive with the presence of an extra scalar degree of freedom. The propagators of both the spin-two and spin-zero modes are positive and well defined. The associated emergent gravitational theory is a bi-gravity theory, as is (secretly) the case in holography. The background metric on which the QFTs are defined, plays the role of dark energy and the emergent theory has always as a solution the original background metric. In the case where the hidden theory is holographic, the overall description yields a higher-dimensional bulk theory coupled to a brane. The effective graviton on the brane has four-dimensional characteristics both in the UV and IR and is always massive.

SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS

AbstractI construct infinitely many nondiffeomorphic examples of $5$ -dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction results for symplectic cobordisms, for which I give a proof not relying on the polyfold abstract perturbation scheme for Symplectic Field Theory (SFT). These results are part of my PhD thesis [23], and are the first applications of higher-dimensional Siefring intersection theory for holomorphic curves and hypersurfaces, as outlined in [23, 24], as a prequel to [30].

From Gaudin Integrable Models to d-Dimensional Multipoint Conformal Blocks.

In this work, we initiate an integrability-based approach to multipoint conformal blocks for higher-dimensional conformal field theories. Our main observation is that conformal blocks for N-point functions may be considered as eigenfunctions of integrable Gaudin Hamiltonians. This provides us with a complete set of differential equations that can be used to evaluate multipoint blocks.

Cobordism conjecture, anomalies, and the String Lamppost Principle

We consider consequences of triviality of cobordism classes and anomaly cancellation in supergravity theories in d > 6. We argue that this leads to the existence of certain defects which we call “I-folds” (a generalization of orientifolds). The requirement that compactifications to lower dimensions involving these defects be anomaly free leads to conditions on the higher dimensional theory. We show that in theories with 16 supercharges in d > 6 this leads to restrictions on the rank of the allowed gauge groups and thus provides an explanation for the observed restrictions in known string theory constructions. In particular, in eight and nine dimensions the only solutions to our constraints are precisely the ones realized in string theory compactifications. We also use these techniques to place constraints on the global structure of the gauge group in eight and nine dimensions.

Static black holes in higher dimensional Einstein–Skyrme models

In this paper we construct a class of hairy static black holes of higher dimensional Einstein-Skyrme theories with the cosmological constant $\Lambda \le 0$ whose scalar is an $SU(2)$ valued field. The spacetime is set to be conformal to $ \mathcal{M}^4 \times \mathcal{N}^{N-4}$ where $\mathcal{M}^4$ and $\mathcal{N}^{N-4}$ are a four dimensional spacetime and a compact Einstein $(N-4)$-dimensional submanifold for $N \ge 5$, respectively, whereas $N=4$ is the trivial case. We discuss the behavior of solutions near the boundaries, namely, near the (event) horizon and in the asymptotic region. Then, we establish local-global existence of black hole solutions and show that black holes with finite energy exist if their geometries are asymptotically Ricci-flat. At the end, we perform a linear stability analysis using perturbative method and give a remark about their stability.

Abnormal Power Consumption Detection Based on Data-Driven

Based on high dimensional random matrix theory and machine learning algorithm, a method to detect abnormal power consumption behaviour of users is proposed. Firstly, the K-means clustering algorithm is used to divide the power loads into load types that obey specific distribution law or with random fluctuation. Then the linear eigenvalue statistics (LES) index can be used to detect the abnormal power consumption behaviour for the former such as unimodal load or bimodal load. And the difference between the actual and predicted value of regression model based on XGBoost algorithm can be used as the basis for judging abnormal power consumption behaviour of the latter. The method proposed in this paper is applicable to different types of loads and can implement a good discriminant effect.

Iterated Laurent series over rings and the Contou-Carrère symbol

This article contains a survey of a new algebro-geometric approach for working with iterated algebraic loop groups associated with iterated Laurent series over arbitrary commutative rings and its applications to the study of the higher-dimensional Contou-Carrère symbol. In addition to the survey, the article also contains new results related to this symbol. The higher-dimensional Contou-Carrère symbol arises naturally when one considers deformation of a flag of algebraic subvarieties of an algebraic variety. The non-triviality of the problem is due to the fact that, in the case , for the group of invertible elements of the algebra of -iterated Laurent series over a ring, no representation is known in the form of an ind-flat scheme over this ring. Therefore, essentially new algebro-geometric constructions, notions, and methods are required. As an application of the new methods used, a description of continuous homomorphisms between algebras of iterated Laurent series over a ring is given, and an invertibility criterion for such endomorphisms is found. It is shown that the higher- dimensional Contou-Carrère symbol, restricted to algebras over the field of rational numbers, is given by a natural explicit formula, and this symbol extends uniquely to all rings. An explicit formula is also given for the higher-dimensional Contou-Carrère symbol in the case of all rings. The connection with higher-dimensional class field theory is described. As a new result, it is shown that the higher-dimensional Contou-Carrère symbol has a universal property. Namely, if one fixes a torsion-free ring and considers a flat group scheme over this ring such that any two points of the scheme are contained in an affine open subset, then after restricting to algebras over the fixed ring, all morphisms from the -iterated algebraic loop group of the Milnor -group of degree to the above group scheme factor through the higher-dimensional Contou-Carrère symbol. Bibliography: 67 titles.

Higher-order non-Hermitian skin effect

The non-Hermitian skin effect is a unique feature of non-Hermitian systems, in which an extensive number of boundary modes appear under the open boundary conditions. Here, we discover higher-order counterparts of the non-Hermitian skin effect that exhibit new boundary physics. In two-dimensional systems with the system size $L \times L$, while the conventional (first-order) skin effect accompanies $O\,( L^{2} )$ skin modes, the second-order skin effect accompanies $O\,( L )$ corner skin modes. This also contrasts with Hermitian second-order topological insulators, in which only $O\,( 1 )$ corner zero modes appear. Moreover, for the third-order skin effect in three dimensions, $O\,( L )$ corner skin modes appear from all $O\,( L^{3} )$ modes. We demonstrate that the higher-order skin effect originates from intrinsic non-Hermitian topology protected by spatial symmetry. We also show that it accompanies the modification of the non-Bloch band theory in higher dimensions.

Rational orbits around 4D Einstein–Lovelock black holes

The orbital dynamics in the strong gravitational field might present unique features of quantum gravity and high-dimensional theory. In this paper, a timelike particle’s periodic orbits around the 4-dimensional Einstein–Lovelock (4 D − EL) black holes are investigated by employing a classification of the zoom–whirl structure with a rational number q . It is found that these rational (periodic) orbits around 4 D − EL black holes have a higher or lower energy than the ones around Schwarzschild black holes during the inspiral stage of detecting the gravitational waves. It depends strongly on the sign of a coupling constant in the theory. These results might provide hints for distinguishing 4 D − EL black holes from Schwarzschild ones by using the orbital dynamical approach in the strong gravitational field.

Horizon Thermodynamics in D-Dimensional f(R) Black Hole.

We consider whether the new horizon-first law works in higher-dimensional theory. We firstly obtain the general formulas to calculate the entropy and the energy of a general spherically-symmetric black hole in D-dimensional theory. For applications, we compute the entropies and the energies of some black hokes in some interesting higher-dimensional theories.

Discrete Hardy Spaces for Bounded Domains in {mathbb {R}}^{n}

Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in {mathbb {R}}^{n}. On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.

Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs

Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge CT, we clarify the properties of stress tensor composite primary operators of minimal twist, [Tm], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling leftlangle {mathcal{O}}_L{mathcal{O}}_Lleft[{T}^mright]rightrangle , where {mathcal{O}}_L is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling leftlangle TT{mathcal{O}}_Lrightrangle , the three-point coupling leftlangle {mathcal{O}}_L{mathcal{O}}_Lleft[{T}^2right]rightrangle is modified at large CT if leftlangle TT{mathcal{O}}_Lrightrangle sim sqrt{C_T} . This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to {mathcal{O}}_L can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.

Equiaffine Braneworld

Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the directions of investigation had, as far as we can discern, all followed the ordinary Euclidean hypersurface theory’s isometric immersion recipe, with the spacetime metric being induced by an ambient parent. We note, in this paper, that the indefinite signature of the Lorentzian metric perhaps hints at the lesser known equiaffine hypersurface theory as being a possibly more natural, i.e., less customized beyond minimal mathematical formalism, description of our universe’s extrinsic geometry. In this alternative, the ambient is deprived of a metric, and the spacetime metric becomes conformal to the second fundamental form of the ordinary theory, therefore is automatically indefinite for hyperbolic shapes. Herein, we advocate investigations in this direction by identifying some potential physical benefits to enlisting the help of equiaffine differential geometry. In particular, we show that a geometric origin for dark energy can be proposed within this framework.

Projective oscillator representations of and

Motivated from understanding higher-dimensional supersymmetric conformal field theory, we study various inhomogeneous oscillator representations of and on supersymmetric polynomial algebras and on spaces of supersymmetric exponential–polynomial functions, analogous to the projective oscillator representations of and . In particular, we find the explicit structures of certain Harish-Chandra modules and Whittaker-type modules of these Lie superalgebras.

3d mirrors of the circle reduction of twisted A2N theories of class S

Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted A2N theories of class S in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.

4D mathcal{N} = 1 Kaluza-Klein superspace

Motivated by recent efforts to encode 11D supergravity in 4D mathcal{N} = 1 superfields, we introduce a general covariant framework relevant for describing any higher dimensional supergravity theory in external 4D mathcal{N} = 1 superspace with n additional internal coordinates. The superspace geometry admits both external and internal diffeomorphisms and provides the superfields necessary to encode the components of the higher dimensional vielbein, except for the purely internal sector, in a universal way that depends only on the internal dimension n. In contrast, the mathcal{N} = 1 superfield content of the internal sector of the metric is expected to be highly case dependent and involve covariant matter superfields, with additional hidden higher dimensional Lorentz and supersymmetry transformations realized in a non-linear manner.

Anomalies, black strings and the charged Cardy formula

We derive the general anomaly polynomial for a class of two-dimensional CFTs arising as twisted compactifications of a higher-dimensional theory on compact manifolds ℳd, including the contribution of the isometries of ℳd. We then use the result to per- form a counting of microstates for electrically charged and rotating supersymmetric black strings in AdS5× S5 and AdS7× S4 with horizon topology BTZt⋉S2 and BTZt⋉S2× {Sigma}_{mathfrak{g}} , respectively, where {Sigma}_{mathfrak{g}} is a Riemann surface. We explicitly construct the latter class of solutions by uplifting a class of four-dimensional rotating black holes. We provide a microscopic explanation of the entropy of such black holes by using a charged version of the Cardy formula.

Cosmological singularities and 2-dimensional dilaton gravity

We study Big-Bang or -Crunch cosmological singularities in 2-dimensional dilaton-gravity-scalar theories, in general obtained by dimensional reduction of higher dimensional theories. The dilaton potential encodes information about the asymptotic data defining the theories, and encompasses various families such as flat space, AdS, conformally AdS as arising from nonconformal branes, and more general nonrelativistic theories. We find a kind of universal near singularity behaviour independent of the dilaton potential, giving universal interrelations between the exponents defining the time behaviour near the cosmological singularity. More detailed analysis using a scaling ansatz enables finding various classes of cosmological backgrounds, recovering known examples such as the AdS Kasner singularity as well finding as new ones. We give some comments on the dual field theory from this point of view.