27,720 research outputs found
Translation and convolution in Clifford analysis
In this paper we study an integral transform in Clifford analysis with a general kernel expressed as an infinite series in terms of Bessel functions and Gegenbauer polynomials. After giving some examples, we construct the inverse of this general transform on the Schwartz space. Moreover, we define a generalized translation operator and four types of generalized convolution associated to the general kernel
Newton's law in braneworlds with an infinite extra dimension
We study the behavior of the fourdimensional Newton's law in warped
braneworlds. The setup considered here is a -brane embedded in
dimensions, where extra dimensions are compactified and a dimension is
infinite. We show that the wave function of gravity is described in terms of
the Bessel functions of -order and that estimate the correction to
Newton's law. In particular, the Newton's law for can be exactly
obtained
Single-centered black hole microstate degeneracies from instantons in supergravity
We obtain holographic constraints on the microscopic degeneracies of black
holes by computing the exact macroscopic quantum entropy using localization,
including the effects of string worldsheet instantons in the supergravity
effective action. For -BPS black holes in type II string theory on , the constraints can be explicitly checked against expressions
for the microscopic BPS counting functions that are known in terms of certain
mock modular forms. We find that the effect of including the infinite sum over
instantons in the holomorphic prepotential of the supergravity leads to a sum
over Bessel functions with successively sub-leading arguments as in the
Rademacher expansion of Jacobi forms -- but begins to disagree with such a
structure near an order where the mock modular nature becomes relevant. This
leads to a systematic method to recover the polar terms of the microscopic
degeneracies from the degeneracy of instantons (the Gromov-Witten invariants).
We check explicitly that our formula agrees with the known microscopic answer
for the first seven values of the magnetic charge invariant.Comment: 32 pages, comments added in v2, submitted to JHE
A Generalisation For The Infinite Integral Over Three Spherical Bessel Functions
A new formula is derived that generalises an earlier result for the infinite
integral over three spherical Bessel functions. The analytical result involves
a finite sum over associated Legendre functions, , of degree and
order . The sum allows for values of that are greater than . A
generalisation for the associated Legendre functions to allow for any rational
for a specific is also shownComment: Published in J. Phys. A: Math. Theor. 43 (2010) 45520
Two-loop Sunset Integrals at Finite Volume
We show how to compute the two-loop sunset integrals at finite volume, for
non-degenerate masses and non-zero momentum. We present results for all
integrals that appear in the Chiral Perturbation Therory (PT) calculation
of the pseudoscalar meson masses and decay constants at NNLO, including the
case of Partially Quenched PT. We also provide numerical implementations
of the finite-volume sunset integrals, and review the results for one-loop
integrals at finite volume.Comment: 45 page
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