We show that the ABJM theory, which is an N = 6 superconformal U(N ) × U(N ) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS 4 /CF T 3 duality at the quantum level. Here we calculate the free energy, and confirm the N 3/2 scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models. *

We study quantum Kähler moduli space of Calabi-Yau fourfolds. Our analysis is based on the recent work by Jockers et al. which gives a novel method to compute the Kähler potential on the quantum Kähler moduli space of Calabi-Yau manifold. In contrast to Calabi-Yau threefold, the quantum nature of higher dimensional Calabi-Yau manifold is yet to be fully elucidated. In this paper we focus on the Calabi-Yau fourfold. In particular, we conjecture the explicit form of the quantum-corrected Kähler potential. We also compute the genus zero Gromov-Witten invariants and test our conjecture by comparing the results with predictions from mirror symmetry. Local toric Calabi-Yau varieties are also discussed. * yhonma@hri.res.in † masahidemanabe@gmail.com Topological string theory gives us a framework to study "topological quantum quantities" as Gromov-Witten invariants corresponding to the worldsheet instanton numbers.Strongly motivated from the string compactification, Calabi-Yau threefolds has been well-studied. The quantum-corrected Kähler potential on the Kähler moduli space of Calabi-Yau threefold can be determined by a single holomorphic function called prepotential which encodes the information about the genus zero Gromov-Witten invariants.This simplification is due to the special Kähler structure of the moduli space of Calabi-Yau threefold [1]. Mirror symmetry is an efficient tool to compute the prepotential as first demonstrated in [2] to the quintic Calabi-Yau threefold. Although moduli spaces of Calabi-Yau manifolds whose complex dimension is greater than three do not have such a special Kähler structure, the higher dimensional mirror symmetry is still useful to compute Gromov-Witten invariants [3, 4, 5] (see also [6]). As pioneered in [7], various Calabi-Yau manifolds can be realized at the IR fixed points of the two dimensional N = (2, 2) gauged linear sigma model (GLSM). Mirror symmetry for Calabi-Yau manifolds described by abelian GLSMs is well understood [8,9] and also proved physically in [10]. However, for general cases with non-abelian gauge groups, comprehensive study of mirror symmetry is yet to come.Recently, it was proposed in [11] that Gromov-Witten invariants of Calabi-Yau manifolds can be computed without using mirror symmetry. More precisely, they proposed the relation e −K = Z GLSM between the exact Kähler potential K on the quantum Kähler moduli space of a Calabi-Yau manifold and the exact partition function Z GLSM of an N = (2, 2) GLSM on S 2 which was computed in [12,13]. This means that we can extract the genus zero Gromov-Witten invariants only from the GLSM calculation. They also checked the consistency of their proposal for some known examples and two physical proofs are given in [14]. Their method is applicable to non-abelian GLSMs and the authors of [11] also made predictions for Gromov-Witten invariants of a determinantal Calabi-Yau threefold. Note that, as mentioned in [11,14], their method has a close relationship to the toric mirror symmetry.The aim of this paper is to study the quant...

We show that the ABJM theory, which is an N = 6 superconformal U(N) × U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS 4 /CF T 3 duality at the quantum level. Here we calculate the free energy, and confirm the N 3/2 scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models. *

We show that the N = 8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N = 6 superconformal U (N ) × U (N ) Chern-Simons-matter theories at level (k, −k). The scaling limit (and Inönü-Wigner contraction) is to scale the trace part of the bifundamental fields as X 0 → λ −1 X 0 and an axial combination of the two gauge fields as B µ → λB µ . Simultaneously we scale the level as k → λ −1 k and then take λ → 0 limit. Interestingly the same constraint equation ∂ 2 X 0 = 0 is derived by imposing finiteness of the action. In this scaling limit, M2-branes are located far from the origin of C 4 /Z k compared to their fluctuations and Z k identification becomes a circle identification. Hence the scaled theory describes N = 8 supersymmetric theory of 2-branes with dynamical coupling. The coupling constant is promoted to a space-time dependent SO(8) vector X I 0 and we show that the scaled theory has a generalized conformal symmetry as well as manifest SO (8) with the transformation of the background fields X I 0 .