University of Alabama Repository :: Browsing by Author "Stern, A."

Browsing by Author "Stern, A."

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BTZ black hole entropy from a Chern-Simons matrix model
(IOP Publishing, 2013-10-30) Chaney, A.; Lu, Lei; Stern, A.; University of Alabama Tuscaloosa
We examine a Chern-Simons matrix model which we propose as a toy model for studying the quantum nature of black holes in 2 + 1 gravity. Its dynamics is described by two N x N matrices, representing the two spatial coordinates. The model possesses an internal SU(N) gauge symmetry, as well as an external rotation symmetry. The latter corresponds to the rotational isometry of the BTZ solution, and does not decouple from SU(N) gauge transformations. The system contains an invariant which is quadratic in the spatial coordinates. We obtain its spectrum and degeneracy, and find that the degeneracy grows exponentially in the large N limit. The usual BTZ black hole entropy formula is recovered upon identifying the quadratic invariant with the square of the black hole horizon radius. The quantum system behaves collectively as an integer (half-integer) spin particle for even (odd) N under 2 pi-rotations.
Fuzzy CP2 spacetimes
(American Physical Society, 2017-02) Chaney, A.; Stern, A.; University of Alabama Tuscaloosa
Four-dimensional manifolds with changing signature are obtained by taking the large N limit of fuzzy CP2 solutions to a Lorentzian matrix model. The regions of Lorentzian signature give toy models of closed universes which exhibit cosmological singularities. These singularities are resolved at finite N, as the underlying CP2 solutions are expressed in terms of finite matrix elements.
Growing hair on the extremal BTZ black hole
(Elsevier, 2017-04-13) Harms, B.; Stern, A.; University of Alabama Tuscaloosa
We show that the nonlinear a-model in an asymptotically AdS(3) space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear a-model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear a-model fields and changes the space-time metric, and it can be used to map the extremal BTZ black hole to infinitely many hairy black hole solutions. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.
Lagrangian formulation for electric charge in a magnetic monopole distribution
(American Physical Society, 2019) Marmo, G.; Scardapane, Emanuela; Stern, A.; Ventriglia, Franco; Vitale, Patrizia; University of Naples Federico II; University of Alabama Tuscaloosa; Istituto Nazionale di Fisica Nucleare (INFN)
We give a Lagrangian description of an electric charge in a field sourced by a continuous magnetic monopole distribution. The description is made possible thanks to a doubling of the configuration space. The Legendre transform of the nonrelativistic Lagrangian agrees with the Hamiltonian description given recently by Kupriyanov and Szabo [Phys. Rev. D 98, 045005 (2018)]. The covariant relativistic version of the Lagrangian is shown to introduce a new gauge symmetry, in addition to standard reparametrizations. The generalization of the system to open strings coupled to a magnetic monopole distribution is also given, as is the generalization to particles in a non-Abelian gauge field which does not satisfy Bianchi identities in some region of the space-time.
Matrix model approach to cosmology
(American Physical Society, 2016-03) Chaney, A.; Lu, Lei; Stern, A.; University of Alabama Tuscaloosa
We perform a systematic search for rotationally invariant cosmological solutions to toy matrix models. These models correspond to the bosonic sector of Lorentzian Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT)-type matrix models in dimensions d less than ten, specifically d = 3 and d = 5. After taking a continuum (or commutative) limit they yield d - 1 dimensional Poisson manifolds. The manifolds have a Lorentzian induced metric which can be associated with closed, open, or static space-times. For d = 3, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a resolution of cosmological singularities, at least within the context of the toy matrix models. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the d = 3 solutions have analogues in higher dimensions. The case of d = 5, in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter dS(4) or anti-de Sitter AdS(4) solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of AdS(4), we find one particular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.
Non-constant non-commutativity in 2d field theories and a new look at fuzzy monopoles
(Elsevier, 2006-06-26) Stern, A.; University of Alabama Tuscaloosa
We write down scalar field theory and gauge theory on two-dimensional non-commutative spaces M with non-vanishing curvature and non-constant non-commutativity. Usual dynamics results upon taking the limit of M going to (i) a commutative manifold M-0 having non-vanishing curvature and (ii) the non-commutative plane. Our procedure does not require introducing singular algebraic maps or frame fields. Rather, we exploit the Kahler structure in the limit (i) and identify the symplectic two-form with the volume two-form. As an example, we take M to be the stereographically projected fuzzy sphere, and find magnetic monopole solutions to the non-commutative Maxwell equations. Although the magnetic charges are conserved, the classical theory does not require that they be quantized. The non-commutative gauge field strength transforms in the usual manner, but the same is not, in general, true for the associated potentials. We develop a perturbation scheme to obtain the expression for gauge transformations about limits (i) and (ii). We also obtain the lowest order Seiberg-Witten map to write down corrections to the commutative field equations and show that solutions to Maxwell theory on M-0 are stable under inclusion of lowest order non-commutative corrections. The results are applied to the example of non-commutative AdS(2). (c) 2006 Elsevier B.V. All rights reserved.
Noncommutative AdS(2)/CFT1 duality: The case of massless scalar fields
(American Physical Society, 2017-09-18) Pinzul, A.; Stern, A.; Universidade de Brasilia; University of Alabama Tuscaloosa
We show how to construct correlators for the CFT1 which is dual to noncommutative AdS(2) (ncAdS(2)). We do it explicitly for the example of the massless scalar field on Euclidean ncAdS(2). ncAdS(2) is the quantization of AdS(2) that preserves all the isometries. It is described in terms of the unitary irreducible representations, more specifically discrete series representations, of so(2, 1). We write down symmetric differential representations for the discrete series and then map them to functions on the Moyal-Weyl plane. The Moyal-Weyl plane has a large distance limit which can be identified with the boundary of ncAdS(2). Killing vectors can be constructed on ncAdS(2) which reduce to the AdS(2) Killing vectors near the boundary. We, therefore, conclude that ncAdS(2) is asymptotically AdS(2), and so the AdS/CFT correspondence should apply. For the example of the massless scalar field on Euclidean ncAdS(2), the on-shell action, and resulting two-point function for the boundary theory, are computed to leading order in the noncommutativity parameter. The computation is nontrivial because nonlocal interactions appear in the Moyal-Weyl description. Nevertheless, the result is remarkably simple and agrees with that of the commutative scalar field theory, up to a rescaling.
Particle dynamics on Snyder space
(Elsevier, 2012-07-01) Lu, Lei; Stern, A.; University of Alabama Tuscaloosa
We examine Hamiltonian formalism on Euclidean Snyder space. The latter corresponds to a lattice in the quantum theory. For any given dynamical system, it may not be possible to identify time with a real number parametrizing the evolution in the quantum theory. The alternative requires the introduction of a dynamical time operator. We obtain the dynamical time operator for the relativistic (nonrelativistic) particle, and use it to construct the generators of Poincare (Galilei) group on Snyder space. (C) 2012 Elsevier B.V. All rights reserved.
Remarks on an exact Seiberg-Witten map
(American Physical Society, 2009-09-24) Stern, A.; University of Alabama Tuscaloosa
We obtain the leading derivative corrections to an expression for the Seiberg-Witten map given by Banerjee and Yang and show how they affect the noncommutative deformation of the Maxwell action, as well as the matter coupling in noncommutative emergent gravity.
Snyder space revisited
(Elsevier, 2012-01-21) Lu, Lei; Stern, A.; University of Alabama Tuscaloosa
We examine basis functions on momentum space for the three-dimensional Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the SO(3) group manifold, and that the basis functions span either one of two Hilbert spaces. This implies the existence of two distinct lattice structures of space. Continuous rotations and translations are unitarily implementable on these lattices. (C) 2011 Elsevier B.V. All rights reserved.
Spinning sigma-model solitons in 2+1 anti-de Sitter space
(Elsevier, 2016-11-04) Harms, B.; Stern, A.; University of Alabama Tuscaloosa
We obtain numerical solutions for rotating topological solitons of the nonlinear s-model in threedimensional anti-de Sitter space. Two types of solutions, i) and ii), are found. The s-model fields are everywhere well defined for both types of solutions, but they differ in their space-time domains. Any time slice of the space-time for the type i) solution has a causal singularity, despite the fact that all scalars constructed from the curvature tensor are bounded functions. No evidence of a horizon is seen for any of the solutions, and therefore the type i) solutions have naked singularities. On the other hand, the space-time domain, along with the fields, for the type ii) solutions are singularity free. Multiple families of solutions exhibiting bifurcation phenomena are found for this case. (C) 2016 The Authors. Published by Elsevier B.V.
Supersymmetric extension of the Snyder algebra
(Elsevier, 2012-04-11) Gouba, L.; Stern, A.; University of Alabama Tuscaloosa; Abdus Salam International Centre for Theoretical Physics (ICTP)
We obtain a minimal supersymmetric extension of the Snyder algebra and study its representations. The construction differs from the general approach given in Hatsuda and Siegel (arXiv:hep-th/0311002) and does not utilize super-de Sitter groups. The spectra of the position operators are discrete. implying a lattice description of space, and the lattice is compatible with supersymmetry transformations. (C) 2011 Elsevier B.V. All rights reserved.

Browsing by Author "Stern, A."

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