Hidehiko Shimada

Proof of all-order finiteness for planar beta-deformed Yang-Mills

We study a marginal deformation of N = 4 Yang–Mills, with a real deformation parameter β. This β-deformed model has only N = 1 supersymmetry and a U(1)×U(1) flavor symmetry. The introduction of a new superspace ⋆-product allows us to formulate the theory in N = 4 light-cone superspace, despite the fact that it has only N = 1 supersymmetry. We show that this deformed theory is conformally invariant, in the planar approximation, by proving that its Green functions are ultra-violet finite to all orders in perturbation theory.

Fuzzy Riemann surfaces

We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.

Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory

Abstract This paper focuses on a three-parameter deformation of N = 4 Yang–Mills that breaks all the supersymmetry in the theory. We show that the resulting non-supersymmetric gauge theory is scale invariant, in the planar approximation, by proving that its Green functions are ultraviolet finite to all orders in light-cone perturbation theory.

On the shape of a D-brane bound state and its topology change

As is well known, coordinates of D-branes are described by N × N matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem, we generalize and elaborate on a simple prescription, first introduced by Hotta, Nishimura and Tsuchiya, which determines the most appropriate gauge to make the separation between diagonal components (D-brane positions) and off-diagonal components. This prescription makes it possible to extract the distribution of D-branes directly from matrices. We verify the power of it by applying it to Monte-Carlo simulations for various lower dimensional Yang-Mills matrix models. In particular, we detect the topology change of the D-brane bound state for a phase transition of a matrix model; the existence of this phase transition is expected from the gauge/gravity duality, and the pattern of the topology change is strikingly similar to the counterpart in the gravity side, the black hole/black string transition. We also propose a criterion, based on the behavior of the off-diagonal components, which determines when our prescription gives a sensible definition of D-brane positions. We provide numerical evidence that our criterion is satisfied for the typical distance between D-branes. For a supersymmetric model, positions of D-branes can be defined even at a shorter distance scale. The behavior of off-diagonal elements found in this analysis gives some support for previous studies of D-brane bound states.

β-deformation for matrix model of M-theory

A new class of deformation of the matrix model of M-theory is considered. The deformation is analogous to the so-called β-deformation of D = 3 + 1, N = 4 super-Yang–Mills theory, which preserves the conformal symmetry. It is shown that the deformed matrix model can be considered as a matrix model of M-theory on a certain curved background in eleven-dimensional supergravity, under a scaling limit involving the deformation parameter and N (the size of the matrices). The background belongs to the so-called pp-wave type metric with a non-constant four-form flux depending linearly on transverse coordinates. Some stable solutions of the deformed model are studied, which correspond to membranes with the torus topology. In particular, it is found that apparently distinct configurations of membranes, having different winding numbers, are indistinguishable in the matrix model. Simultaneous introduction of both β-deformation and mass-deformation is also considered, and, in particular, a situation is found in which the stable membrane configuration interpolates between a torus and a sphere, depending on the values of the deformation parameters.

Holography at string field theory level: Conformal three point functions of BMN operators

Abstract We propose a general framework for applying the pp-wave approximation to holographic calculation in the AdS/CFT correspondence. By assuming the existence and some properties of string field theory (SFT) on the AdS 5 × S 5 background, we extend the holographic ansatz proposed by Gubser, Klebanov, Polyakov and by Witten to the SFT level. We extract relevant information about assumed SFT on AdS 5 × S 5 from its approximation, pp-wave SFT. As an explicit example, we study conformal three point functions of BMN operators. We find a new formula which expresses a three point function as an infinite series of matrix elements of the SFT vertex. We identify a broad class of field redefinitions which do not affect the final observable. Known ambiguity in the pp-wave SFT vertex is due to a particular redefinition in this class. Under these redefinitions, matrix elements themselves change, but the sum of the series is invariant due to a non-trivial cancellation. The result agrees with that previously calculated in gauge theory.

Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3

Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3 Stefano Kovacs1,∗, Yuki Sato2,3,4,∗, and Hidehiko Shimada5 1Dublin Institute for Advanced Studies, Dublin, Ireland 2 National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics, University of the Witwartersrand, WITS 2050, South Africa 3High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan 4Department of Particle and Nuclear Physics, Graduate University for Advanced Studies (SOKENDAI), Tsukuba, Ibaraki 305-0801, Japan 5Okayama Institute for Quantum Physics, Okayama, Japan ∗E-mail: skovacs@stp.dias.ie, satoyuki@post.kek.jp, shimada.hidehiko@googlemail.com

On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang–Mills theory

Abstract We study the commutative limit of the non-commutative maximally supersymmetric Yang–Mills theory in four dimensions ( N = 4 SYM ), where non-commutativity is introduced in the two spacelike directions. The commutative limits of non-commutative spaces are important in particular in the applications of non-commutative spaces for regularisation of supersymmetric theories (such as the use of non-commutative spaces as alternatives to lattices for supersymmetric gauge theories and interpretations of some matrix models as regularised supermembrane or superstring theories), which in turn can play a prominent role in the study of quantum gravity via the gauge/gravity duality. In general, the commutative limits are known to be singular and non-smooth due to UV/IR mixing effects. We give a direct proof that UV effects do not break the continuity of the commutative limit of the non-commutative N = 4 SYM to all order in perturbation theory, including non-planar contributions. This is achieved by establishing the uniform convergence (with respect to the non-commutative parameter) of momentum integrals associated with all Feynman diagrams appearing in the theory, using the same tools involved in the proof of finiteness of the commutative N = 4 SYM .

On membrane interactions and a three-dimensional analog of Riemann surfaces

A bstractMembranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.

Simple variables for AdS

We introduce simple variables for describing the AdS