scholarly journals Higher spin wormholes from modular bootstrap

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Diptarka Das ◽  
Shouvik Datta
Keyword(s):  
Form Factor ◽  
Partition Function ◽  
Power Law ◽  
Spectral Form ◽  
Ensemble Averaging ◽  
Level Statistics ◽  
Higher Spin ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles ◽  
Euclidean Wormhole

Abstract We investigate the connection between spacetime wormholes and ensemble averaging in the context of higher spin AdS3/CFT2. Using techniques from modular bootstrap combined with some holographic inputs, we evaluate the partition function of a Euclidean wormhole in AdS3 higher spin gravity. The fixed spin sectors of the dual CFT2 exhibit features that starkly go beyond conventional random matrix ensembles: power-law ramps in the spectral form factor and potentials with a double-well/crest underlying the level statistics.

scholarly journals Integrability and spectral form factor in Chern–Simons formulation

2020 ◽  
Vol 35 (24) ◽  
pp. 2050143
Author(s):  
Chen-Te Ma ◽  
Hongfei Shu
Keyword(s):  
Form Factor ◽  
Random Matrix ◽  
Integrable Model ◽  
Toda Chain ◽  
Simons Theory ◽  
Spectral Form ◽  
Higher Spin ◽  
Chain Theory ◽  
Matrix Spectrum ◽  
Chern Simons

We study the integrability from the spectral form factor in the Chern–Simons formulation. The effective action in the higher spin sector was not derived so far. Therefore, we begin from the SL(3) Chern–Simons higher spin theory. Then the dimensional reduction in this Chern–Simons theory gives the SL(3) reparametrization invariant Schwarzian theory, which is the boundary theory of an interacting theory between the spin-2 and spin-3 fields at the infrared or massless limit. We show that the Lorentzian SL(3) Schwarzian theory is dual to the integrable model, SL(3) open Toda chain theory. Finally, we demonstrate the application of open Toda chain theory from the SL(2) case. The numerical result shows that the spectral form factor loses the dip-ramp-plateau behavior, consistent with integrability. The spectrum is not a Gaussian random matrix spectrum. We also give an exact solution of the spectral form factor for the SL(3) theory. This solution provides a similar form to the SL(2) case for [Formula: see text]. Hence the SL(3) theory should also do not have a Gaussian random matrix spectrum.

scholarly journals Sensitivity of the spectral form factor to short-range level statistics

2020 ◽  
Vol 102 (4) ◽  
Author(s):  
Wouter Buijsman ◽  
Vadim Cheianov ◽  
Vladimir Gritsev
Keyword(s):  
Form Factor ◽  
Short Range ◽  
Spectral Form ◽  
Level Statistics

scholarly journals Summing over geometries in string theory

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lorenz Eberhardt
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Moduli Space ◽  
Ensemble Averaging ◽  
Canonical Partition Function ◽  
Conformal Boundary ◽  
Grand Canonical Partition Function ◽  
The Family ◽  
Grand Canonical ◽  
Euclidean Wormhole

Abstract We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on $$ {\mathrm{\mathcal{M}}}_3\times {\mathrm{S}}^3\times {\mathbbm{T}}^4 $$ ℳ 3 × S 3 × T 4 (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). We strengthen the analysis of [1] and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries. We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime. Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ3. We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕N SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’. We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries. We also briefly discuss the effect of ensemble averaging over the Narain moduli space of $$ {\mathbbm{T}}^4 $$ T 4 and of deforming away from the orbifold by the marginal deformation.

Level Spacing Distributions of Random Matrix Ensembles

1993 ◽  
Vol 62 (7) ◽  
pp. 2248-2259 ◽  
Author(s):  
Masahiro Shiroishi ◽  
Taro Nagao ◽  
Miki Wadati
Keyword(s):  
Random Matrix ◽  
Level Spacing ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles
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