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Register a new userThe Large $N$ Limit of icMERA and Holography
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In this work we compute the entanglement entropy in continuous icMERA tensor networks for large $N$ models at strong coupling. Our results show that the $1/N$ quantum corrections to the Fisher information metric (interpreted as a local bond dimension of the tensor network) in an icMERA circuit, can be related to quantum corrections to the minimal area surface in the the Ryu-Takayanagi formula. Upon picking two different non-Gaussian entanglers to build the icMERA circuit, the results for the entanglement entropy only differ at subleading orders in $1/G_N$, i.e., at the structure of the quantum corrections in the bulk. The fact that the large $N$ part of the entropy can be always related to the leading area term of the holographic calculation results thus very suggestive. These results, which to our knowledge suppose the first tensor network calculations at large $N$ and strong coupling, pave the road for using tensor networks to describe the emergence of continuous spacetime geometries from the the structure of entanglement in quantum field theory.
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Quantum decoherence is the loss of a systems purity due to its interaction with the surrounding environment. Via the AdS/CFT correspondence, we study how a system decoheres when its environment is a strongly-coupled theory. In the Feynman-Vernon formalism, we compute the influence functional holographically by relating it to the generating function of Schwinger-Keldysh propagators and thereby obtain the dynamics of the systems density matrix. We present two exactly solvable examples: (1) a straight string in a BTZ black hole and (2) a scalar probe in AdS$_5$. We prepare an initial state that mimics Schrodingers cat and identify different stages of its decoherence process using the time-scaling behaviors of Renyi entropy. We also relate decoherence to local quantum quenches, and by comparing the time evolution behaviors of the Wigner function and Renyi entropy we demonstrate that the relaxation of local quantum excitations leads to the collapse of its wave-function.
This is the contribution to Quarks2018 conference proceedings. This contribution is devoted to the holographic description of chaos and quantum complexity in the strongly interacting systems out of equilibrium. In the first part of the talk we present different holographic complexity proposals in out-of-equilibrium CFT following the local perturbation. The second part is devoted to the chaotic growth of the local operator size at a finite chemical potential. There are numerous results stating that the chemical potential may lead to the chaos disappearance, and we confirm these results from holographic viewpoint.
We study $mathcal{N}=1$ supersymmetric three-dimensional Quantum Electrodynamics with $N_f$ two-component fermions. Due to the infra-red (IR) softening of the photon, $ep$-scalar and photino propagators, the theory flows to an interacting fixed point deep in the IR, $p_E ll e^2 N_f/8$, where $p_E$ is the euclidean momentum and $e$ the electric charge. At next-to-leading order in the $1/N_f$-expansion, we find that the flow of the dimensionless effective coupling constant $overline{al}$ is such that: $overline{al} ra 8/big(N_f ,(1+C/N_f)big) approx (8/N_f)(1-0.4317/N_f)$ where $C= 2,(12-pi^2)/pi^2$. Hence, the non-trivial IR fixed point is stable with respect to quantum corrections. Various properties of the theory are explored and related via a mapping to the ones of a $mathcal{N}=1$ model of super-graphene. In particular, we derive the interaction correction coefficient to the optical conductivity of super-graphene, $C_{rm sg} = (12-pi^2)/(2pi) = 0.3391$, which is six times larger than in the non-supersymmetric case, $C_{rm g} = (92-9pi^2)/(18pi) = 0.0561$.
We propose a general formula for the perturbative large N superconformal index of 5d quiver fixed point theories that have an AdS(6)xS(4)/Z(n) supergravity dual. This index is obtained from the parent theory by projecting to orbifold-invariant states and adding the twisted sector contributions. Our result agrees with expectations from the dual supergravity description. We test our formula against the direct computation of the index for Z(2) and Z(3) and find complete agreement.
In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in $D = 4$ space-time dimensions. We show that such a symmetry-breaking indeed occurs in certain families of non-supersymmetric large $N$ gauge theories at a planar limit. We also show that this phenomenon is accompanied by the system remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature. These analyses are motivated by the work done in arXiv:2005.03676 where symmetry-breaking was observed in all thermal states for certain CFTs in fractional dimensions. In our case, the theories demonstrating the above features have gauge groups which are specific products of $SO(N)$ in one family and $SU(N)$ in the other. Working in a perturbative regime at the $Nrightarrowinfty$ limit, we show that the beta functions in these theories yield circles of fixed points in the space of couplings. We explicitly check this structure up to two loops and then present a proof of its survival under all loop corrections. We show that under certain conditions, an interval on this circle of fixed points demonstrates both the spontaneous breaking of a global symmetry as well as a persistent BEH phase at all nonzero temperatures. The broken global symmetry is $mathbb{Z}_2$ in one family of theories and $U(1)$ in the other. The corresponding order parameters are expectation values of the determinants of bifundamental scalar fields in these theories. We characterize these symmetries as baryon-like symmetries in the respective models.
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