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Register a new userLarge-$N$ limit as a second quantization
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Authors
Masanori Hanada
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We propose a simple geometric interpretation for gauge/gravity duality, that relates the large-$N$ limit of gauge theory to the second quantization of string theory.
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We consider a new large-N limit, in which the t Hooft coupling grows with N. We argue that a class of large-N equivalences, which is known to hold in the t Hooft limit, can be extended to this very strongly coupled limit. Hence this limit may lead to a new way of studying corrections to the t Hooft limit, while keeping nice properties of the latter. As a concrete example, we describe large-N equivalences between the ABJM theory and its orientifold projection. The equivalence implies that operators neutral under the projection symmetry have the same correlation functions in two theories at large-N. Usual field theory arguments are valid when t Hooft coupling $lambdasim N/k$ is fixed and observables can be computed by using a planar diagrammatic expansion. With the help of the AdS/CFT correspondence, we argue that the equivalence extends to stronger coupling regions, $Ngg k$, including the M-theory region $Ngg k^5$. We further argue that the orbifold/orientifold equivalences between certain Yang-Mills theories can also be generalized. Such equivalences can be tested both analytically and numerically. Based on calculations of the free energy, we conjecture that the equivalences hold because planar dominance persists beyond the t Hooft limit.
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.
We show how a recently proposed large $N$ duality in the context of type IIA strings with ${cal N}=1$ supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIA strings in M-theory. The phase structure of M-theory on $G_2$ holonomy manifolds and an $S^3$ flop are the key ingredients in this derivation.
We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background. We then study the behaviour of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on S^4 at large N localises around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant.
Noncompact SO(1,N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d geq 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented to next to leading order on a finite lattice. The dynamically generated gap is negative and serves as a coupling-dependent infrared regulator which vanishes in the limit of infinite lattice size. The cancellation of infrared divergences in invariant correlation functions in this limit is nontrivial and is in d=2 demonstrated by explicit computation for the above quantities. For the Binder cumulant the thermodynamic limit is finite and is given by 2/(N+1) in the order considered. Monte Carlo simulations suggest that the remainder is small or zero. The potential implications for ``criticality and ``triviality of the theories in the SO(1,N) invariant sector are discussed.
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