arXiv subjects

Hidehiko Shimada

Publications and source records attributed to Hidehiko Shimada.

17 recordsLinked to original sources

arXiv2024

A new perspective on thermal transition in QCD

Motivated by the picture of partial deconfinement developed in recent years for large-$N$ gauge theories, we propose a new way of analyzing and understanding thermal phase transition in QCD. We find nontrivial support for our proposal by analyzing the WHOT-QCD collaboration's lattice configurations for SU(3) QCD in $3+1$ spacetime dimensions with up, down, and strange quarks. We find that the Polyakov line (the holonomy matrix around a thermal time circle) is governed by the Haar-random distribution at low temperatures. The deviation from the Haar-random distribution at higher temperatures can be measured via the character expansion, or equivalently, via the expectation values of the Polyakov loop defined by the various nontrivial representations of SU(3). We find that the Polyakov loop corresponding to the fundamental representation and loops in the higher representation condense at different temperatures. This suggests that there are (at least) three phases, one intermediate phase existing in between the completely-confined and the completely-deconfined phases. Our identification of the intermediate phase is supported also by the condensation of instantons: by studying the instanton numbers of the WHOT-QCD configurations, we find that the instanton condensation occurs for temperature regimes corresponding to what we identify as the completely-confined and intermediate phases, whereas the instantons do not condense in the completely-deconfined phase. Our characterization of confinement based on the Haar-randomness explains why the Polyakov loop is a good observable to distinguish the confinement and the deconfinement phases in QCD despite the absence of the $\mathbb{Z}_3$ center symmetry.

hep-th↗

arXiv2023

Partial deconfinement in QCD at $N=3$ and $N=\infty$

We describe how the general mechanism of partial deconfinement applies to large-$N$ QCD and the partially-deconfined phase inevitably appears between completely-confined and completely-deconfined phases. Furthermore, we propose how the partial deconfinement can be observed in the real-world QCD with SU(3) gauge group. We propose the relationship between the behaviors of the Polyakov loop and other quantities. We test our proposal against lattice simulation data and find a nontrivial matching.

hep-lat↗

arXiv2021

Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance

We identify a nontrivial yet tractable quantum field theory model with space/time anisotropic scale invariance, for which one can exactly compute certain four-point correlation functions and their decompositions via the operator-product expansion(OPE). The model is the Calogero model, non-relativistic particles interacting with a pair potential $\frac{g}{|x-y|^2}$ in one dimension, considered as a quantum field theory in one space and one time dimension via the second quantisation. This model has the anisotropic scale symmetry with the anisotropy exponent $z=2$. The symmetry is also enhanced to the Schrödinger symmetry. The model has one coupling constant $g$ and thus provides an example of a fixed line in the renormalisation group flow of anisotropic theories. We exactly compute a nontrivial four-point function of the fundamental fields of the theory. We decompose the four-point function via OPE in two different ways, thereby explicitly verifying the associativity of OPE for the first time for an interacting quantum field theory with anisotropic scale invariance. From the decompositions, one can read off the OPE coefficients and the scaling dimensions of the operators appearing in the intermediate channels. One of the decompositions is given by a convergent series, and only one primary operator and its descendants appear in the OPE. The scaling dimension of the primary operator we computed depends on the coupling constant. The dimension correctly reproduces the value expected from the well-known spectrum of the Calogero model combined with the so-called state-operator map which is valid for theories with the Schrödinger symmetry. The other decomposition is given by an asymptotic series. The asymptotic series comes with exponentially small correction terms, which also have a natural interpretation in terms of OPE.

hep-th↗

arXiv2021

Color Confinement and Bose-Einstein Condensation

We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from $N^0$ to $N^2$, which persists in the weak coupling region. Indistinguishability associated with the symmetry group -- SU($N$) or O($N$) in gauge theory, and S$_N$ permutations in the system of identical bosons -- is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite $N$, and for quantum gravity via gauge/gravity duality.

hep-th↗

arXiv2018

Towards a tensionless string field theory for the N=(2,0) CFT in d=6

We describe progress in using the field theory of tensionless strings to arrive at a Lagrangian for the six-dimensional $\mathcal N=(2,0)$ conformal theory. We construct the free part of the theory and propose an ansatz for the cubic vertex in light-cone superspace. By requiring closure of the $(2,0)$ supersymmetry algebra, we fix the cubic vertex up to two parameters.

hep-th↗

arXiv2018

Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

hep-th↗

arXiv2015

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

Membranes 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 R^3 connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.

hep-th↗

arXiv2015

Simple variables for AdS$_5 \times S^5$ superspace

We introduce simple variables for describing the AdS$_5\times S^5$ superspace, i. e. $\frac{PSU(2,2|4)}{SO(4,1)\times SO(5)}$. The idea is to embed the coset superspace into a space described by variables which are in linear (ray) representations of the supergroup $PSU(2,2|4)$ by imposing certain supersymmetric quadratic constraints (up to two overall U(1) factors). The construction can be considered as a supersymmetric generalisation of the elementary realisations of the $AdS_5$ and the $S^5$ spaces by the SO(4,2) and SO(6) invariant quadratic constraints on two six-dimensional flat spaces.

hep-th↗

arXiv2014

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

We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). 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.

hep-th↗

arXiv2014

Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3

We consider states with large angular momentum to facilitate the study of the M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes the gravity side difficult, while the CFT is strongly coupled and the planar approximation is not applicable. To overcome these difficulties, we focus on states on the gravity side with large angular momentum J>>1 and identify the dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this sector. Natural approximation schemes arise on both sides thanks to the presence of the small parameter 1/J. On the AdS side, we use the matrix model of M-theory on the maximally supersymmetric pp-wave background with matrices of size J/k. A perturbative treatment of this matrix model provides a good approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer type expansion arises naturally for large J in spite of the theory being strongly coupled. The energy spectra on the two sides agree at leading order. This provides a non-trivial test of the AdS_4/CFT_3 correspondence including near-BPS observables associated with membrane degrees of freedom, thus verifying the duality beyond the previously studied sectors corresponding to either BPS observables or the type IIA string regime.

hep-th↗

arXiv2012

On a new type of orbifold equivalence and M-theoretic AdS4/CFT3 duality

We consider the large-N limit of \mathcal{N}=6 U(N) \times U(N) superconformal Chern-Simons (ABJM) theory with fixed level k, which is conjectured to be dual to M-theory on AdS4\times (S^7/Z_k) background. We point out that the so-called orbifold equivalence on the gravity side, combined with the AdS4/CFT3 duality, predicts a hitherto unknown type of duality on the gauge theory side. It establishes the equivalence between a class of observables, which are not necessarily protected by supersymmetry, in strongly coupled ABJM theories away from the planar approximation, with different values of k and N but sharing common kN. This limit is vastly different from the planar limit, and hence from the gauge theory point of view the duality is more difficult to explain compared to the previously known analogous equivalence between planar gauge theories, where one can explicitly prove the equivalence diagrammatically using the dominance of the planar diagrams.

hep-th↗

arXiv2009

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

As is well known, coordinates of D-branes are described by NxN 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.

hep-th↗

arXiv2008

$β$-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 $\b$-deformation of $D=3+1$, $\mN=4$ 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 $\b$-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.

hep-th↗

arXiv2007

Noncommutative Riemann Surfaces

We introduce C-Algebras of compact Riemann surfaces $Σ$ as non-commutative analogues of the Poisson algebra of smooth functions on $Σ$. Representations of these algebras give rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as $N\to\infty$. For a particular class of surfaces, nicely interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras.

math-ph↗

arXiv2007

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

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 ultra-violet finite to all orders in light-cone perturbation theory.

hep-th↗

arXiv2007

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 beta. This beta-deformed model has only N=1 supersymmetry and a U(1)xU(1) flavor symmetry. The introduction of a new superspace star-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.

hep-th↗

arXiv2004

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

A general framework for applying the pp-wave approximation to holographic calculations in the AdS/CFT correspondence is proposed. By assuming the existence and some properties of string field theory (SFT) on $AdS_5 \times S^5$ background, we extend the holographic ansatz proposed by Gubser, Klebanov, Polyakov and Witten to SFT level. We extract relevant information of assumed SFT on $AdS_5 \times S^5$ from its approximation, pp-wave SFT. As an explicit example, we perform string theoretic calculations of the conformal three point functions of the BMN operators. The results agree with the previous calculations in gauge theory. We identify a broad class of field redefinitions, including known ambiguities of the interaction Hamiltonian, which does not affect the results.

hep-th↗