ترغب بنشر مسار تعليمي؟ اضغط هنا

Wormholes and Spectral Statistics in the Narain Ensemble

65   0   0.0 ( 0 )
 نشر من قبل Scott Collier
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We study the spectral statistics of primary operators in the recently formulated ensemble average of Narains family of free boson conformal field theories, which provides an explicit (though exotic) example of an averaged holographic duality. In particular we study moments of the partition function by explicit computation of higher-degree Eisenstein series. This describes the analog of wormhole contributions coming from a sum of over geometries in the dual theory of U(1) gravity in AdS$_3$. We give an exact formula for the two-point correlation function of the density of primary states. We compute the spectral form factor and show that the wormhole sum reproduces precisely the late time plateau behaviour related to the discreteness of the spectrum. The spectral form factor does not exhibit a linear ramp.



قيم البحث

اقرأ أيضاً

For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper we analyse the time depen dence of correlation functions of operators. We study them in the ergodic limit as well as their approach to the ergodic limit which is controlled by non-universal massive modes. An effective field theory (EFT) corresponding to the causal symmetry and its breaking describes the ergodic phase. We demonstrate that the resulting Goldstone-mode theory has a topological expansion, analogous to the one described in arXiv:2008.02271 with added operator sources, whose leading non-trivial topologies give rise to the universal ramp seen in correlation functions. The ergodic behaviour of operators in our EFT is seen to result from a combination of RMT-like spectral statistics and Haar averaging over wave-functions. Furthermore we analytically capture the plateau behaviour by taking into account the contribution of a second saddle point. Our main interest are quantum many-body systems with holographic duals and we explicitly establish the validity of the EFT description in the SYK-class of models, starting from their microscopic description. By studying the tower of massive modes above the Goldstone sector we get a detailed understanding of how the ergodic EFT phase is approached and derive the relevant Thouless time scales. We point out that the topological expansion can be reinterpreted in terms of contributions of bulk wormholes and baby-universes.
We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the Eigenstate Thermalization Hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS$_3$, including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of factorization in products of partition functions.
We generalize the holographic correspondence between topological gravity coupled to an abelian Chern-Simons theory in three dimensions and an ensemble average of Narains family of massless free bosons in two dimensions, discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the correspondence also works for toroidal orbifolds but not for K3 or Calabi-Yau sigma-models and not always for the minimal models. We conjecture that the correspondence requires that the central charge is equal to the critical central charge defined by the asymptotic density of states of the chiral algebra. For toroidal orbifolds, we extend the holographic correspondence to correlation functions of twist operators by using topological properties of rational tangles in the three-dimensional ball, which represent configurations of vortices associated to a discrete gauge symmetry.
We discuss the holographic description of Narain $U(1)^ctimes U(1)^c$ conformal field theories, and their potential similarity to conventional weakly coupled gravity in the bulk, in the sense that the effective IR bulk description includes $U(1)$ gra vity amended with additional light degrees of freedom. Starting from this picture, we formulate the hypothesis that in the large central charge limit the density of states of any Narain theory is bounded by below by the density of states of $U(1)$ gravity. This immediately implies that the maximal value of the spectral gap for primary fields is $Delta_1=c/(2pi e)$. To test the self-consistency of this proposal, we study its implications using chiral lattice CFTs and CFTs based on quantum stabilizer codes. First we notice that the conjecture yields a new bound on quantum stabilizer codes, which is compatible with previously known bounds in the literature. We proceed to discuss the variance of the density of states, which for consistency must be vanishingly small in the large-$c$ limit. We consider ensembles of code and chiral theories and show that in both cases the density variance is exponentially small in the central charge.
105 - Edward A. Olszewski 2015
We construct dyon solutions on a collection of coincident D4-branes, obtained by applying the group of T-duality transformations to a type I SO(32) superstring theory in 10 dimensions. The dyon solutions, which are exact, are obtained from an action consisting of the non-abelian Dirac-Born-Infeld action and Wess-Zumino-like action. When one of the spatial dimensions of the D4-branes is taken to be vanishingly small, the dyons are analogous to the t Hooft/Polyakov monopole residing in a 3+1 dimensional spacetime, where the component of the Yang-Mills potential transforming as a Lorentz scalar is re-interpreted as a Higgs boson transforming in the adjoint representation of the gauge group. We next apply a T-duality transformation to the vanishingly small spatial dimension. The result is a collection of D3-branes not all of which are coincident. Two of the D3-branes which are separated from the others acquire intrinsic, finite, curvature and are connected by a wormhole. The dyon possesses electric and magnetic charges whose values on each D3-brane are the negative of one another. The gravitational effects, which arise after the T-duality transformation, occur despite the fact that the Lagrangian density from which the dyon solutions have been obtained does not explicitly include the gravitational interaction. These solutions provide a simple example of the subtle relationship between the Yang-Mills and gravitational interactions, i.e. gauge/gravity duality.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا