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We present string-theory derivation of the semiclassical entropy of extremal dyonic black holes in the approach based on conformal sigma model (NS-NS embedding of the classical solution). We demonstrate (resolving some puzzles existed in…
It has been recently conjectured that the spectral determinants of operators associated to mirror curves can be expressed in terms of a generalization of theta functions, called quantum theta functions. In this paper we study the symplectic…
We continue the study of a special entry in the AdS/CFT dictionary, namely a holographic formula relating the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter (ALAdS) space to a relative…
We present a method which allows to deform extremal black hole solutions into non-extremal solutions, for a large class of supersymmetric and non-supersymmetric Einstein-Vector-Scalar type theories. The deformation is shown to be largely…
We study various properties of a nonperturbative partition function which can be associated to any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix…
Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…
In this work we explore a numerical technique, based on the spherical harmonic decomposition and the discretization of the radial coordinate through \v{C}eby\v{s}\"ev polynomial interpolation, for the computation of quasi-bound states of…
The attractor mechanism is usually thought of as the fixing of the near horizon moduli of a BPS black hole in terms of conserved charges measured at infinity. Recent progress in understanding BPS solutions in five dimensions indicates that…
There is ample evidence that the bulk dual of a $T\overline{T}$ deformed holographic CFT is a gravitational system with a finite area cutoff boundary. For states dual to black holes, the finite cutoff surface cannot be moved beyond the…
We introduce, in a systematic way, a set of generating functions that solve all the different combinatorial problems that crop up in the study of black hole entropy in Loop Quantum Gravity. Specifically we give generating functions for: The…
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free $\omega$ parameter. For a negative…
We investigate properties of zeta functions of polynomial rings and their quotients, generalizing and extending some classical results about Dedekind zeta functions of number fields. By an application of Delange's version of the Ikehara…
We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an…
We study static BPS black hole horizons in four dimensional N=2 gauged supergravity coupled to $n_v$-vector multiplets and with an arbitrary cubic prepotential. We work in a symplectically covariant formalism which allows for both electric…
On a manifold with boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of…
We study discrete (duality) symmetries of functional determinants. An exact transformation of the effective action under the inversion of background fields $\beta (x) \to \beta^{-1}(x)$ is found. We show that in many cases this inversion…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
We consider a class of 4D supersymmetric black hole solutions, arising from string theory compactifications, which classically have vanishing horizon area and singular space-time geometry. String theory motivates the inclusion of higher…
The functional potential formalism is used to analyze stationary axisymmetric spaces in the Einstein-Maxwell-Dilaton theory. Performing a Legendre transformation, a ``Hamiltonian''is obtained, which allows to rewrite the dynamical equations…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…