scholarly journals AdS one-loop partition functions from bulk and edge characters

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Zimo Sun
Keyword(s):  
Partition Function ◽  
Integral Representation ◽  
Integral Transform ◽  
Integral Formula ◽  
Partition Functions ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Higher Spin ◽  
The One

Abstract We show that the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss the relation between the character integral representation and the Rindler-AdS thermal partition function.

scholarly journals Supersymmetric localization on dS: sum over topologies

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Rudranil Basu ◽  
Augniva Ray
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Higher Spin Gravity ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Higher Spin ◽  
3D Gravity ◽  
Chern Simons ◽  
Perturbative Result

AbstractWe find the exact quantum gravity partition function on the static patch of 3d de Sitter spacetime. We have worked in the Chern Simons formulation of 3d gravity. To obtain a non-perturbative result, we supersymmetrized the Chern Simons action and used the technique of supersymmetric localization. We have obtained an exact non-perturbative result for the spin-2 gravity case. We comment on the divergences present in the theory. We also comment on higher spin gravity theories and analyse the nature of divergences present in such theories.

scholarly journals Partition functions of p-forms from Harish-Chandra characters

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Justin R. David ◽  
Jyotirmoy Mukherjee
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Integral Representation ◽  
Integral Transform ◽  
Entanglement Entropy ◽  
Integral Transforms ◽  
Partition Functions ◽  
De Sitter ◽  
Symmetric Tensors ◽  
Hyperbolic Cylinders

Abstract We show that the determinant of the co-exact p-form on spheres and anti-de Sitter spaces can be written as an integral transform of bulk and edge Harish-Chandra characters. The edge character of a co-exact p-form contains characters of anti-symmetric tensors of rank lower to p all the way to the zero-form. Using this result we evaluate the partition function of p-forms and demonstrate that they obey known properties under Hodge duality. We show that the partition function of conformal forms in even d + 1 dimensions, on hyperbolic cylinders can be written as integral transforms involving only the bulk characters. This supports earlier observations that entanglement entropy evaluated using partition functions on hyperbolic cylinders do not contain contributions from the edge modes. For conformal coupled scalars we demonstrate that the character integral representation of the free energy on hyperbolic cylinders and branched spheres coincide. Finally we propose a character integral representation for the partition function of p-forms on branched spheres.

CHARGED BLACK HOLES IN ASYMPTOTICALLY ANTI-DE SITTER SPACETIME

2000 ◽  
Vol 14 (19n20) ◽  
pp. 1953-1966 ◽  
Author(s):  
P. MITRA
Keyword(s):  
Black Holes ◽  
Functional Integral ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
One Dimensional ◽  
Sitter Spacetime ◽  
Zero Entropy ◽  
Usual Case ◽  
The One ◽  
Extremal Black Holes

Unlike the extremal Reissner–Nordström black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if (functional integral) quantization is carried out after extremalization. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case. This is because the functional integral is dominated by non-extremal configurations of lower action. However, some special non-extremal black holes have higher action and may decay into extremal configurations. An attempt is also made to see if the anti-de Sitter version can be described by a microscopic model consisting of a one-dimensional gas of massless particles as in the usual case. Such a description is possible only in the limit of vanishing cosmological constant.

scholarly journals A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Makram Hamouda ◽  
Mohamed Ali Hamza ◽  
Alessandro Palmieri
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Integral Transform ◽  
Global Solutions ◽  
Representation Formula ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Semilinear Wave Equation ◽  
Sitter Spacetime ◽  
Derivative Type

<p style='text-indent:20px;'>In this paper, we establish blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime with nonlinearity of derivative type. Our approach is based on the integral representation formula for the solution to the corresponding linear problem in the one-dimensional case, that we will determine through Yagdjian's Integral Transform approach. As upper bound for the exponent of the nonlinear term, we discover a Glassey-type exponent which depends both on the space dimension and on the Lorentzian metric in the generalized Einstein-de Sitter spacetime.</p>

scholarly journals THE FREE DIRAC SPINORS OF THE SPIN BASIS ON THE DE SITTER EXPANDING UNIVERSE

2011 ◽  
Vol 26 (22) ◽  
pp. 1613-1619 ◽  
Author(s):  
ION I. COTĂESCU
Keyword(s):  
Energy Operator ◽  
Global Behavior ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Specific Term ◽  
Sitter Spacetime ◽  
The One ◽  
Phase Functions ◽  
Spin Basis ◽  
Dirac Spinors

It is shown that on the de Sitter spacetime the global behavior of the free Dirac spinors in momentum representation is determined by several phase factors which are functions of momentum with special properties. Such suitable phase functions can be chosen for writing down the free Dirac quantum modes of the spin basis that are well-defined even for the particles at rest in the moving local charts where the modes of the helicity basis remain undefined. Under quantization, these modes lead to a basis in which the one-particle operators keep their usual forms apart from the energy operator which lays out a specific term depending on the concrete phase function one uses.

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Wavefunctions in dS/CFT revisited: principal series and double-trace deformations

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hiroshi Isono ◽  
Hoiki Madison Liu ◽  
Toshifumi Noumi
Keyword(s):  
Principal Series ◽  
Light Fields ◽  
Quadratic Term ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Complementary Series ◽  
Point Function ◽  
Sitter Spacetime ◽  
Simple Scaling

Abstract We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to the situation in nonrelativistic AdS/CFT with a bulk scalar whose mass squared is below the Breitenlohner-Freedman (BF) bound. We also provide a new dS/CFT dictionary relating de Sitter two-point functions and conformal two-point functions in the would-be dual CFT.

scholarly journals Interacting quantum fields in various charts of anti–de Sitter spacetime

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
E. T. Akhmedov ◽  
A. A. Artemev ◽  
I. V. Kochergin
Keyword(s):  
De Sitter Spacetime ◽  
Quantum Fields ◽  
De Sitter ◽  
Sitter Spacetime
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