arXiv subjects

Hisayoshi Muraki

Publications and source records attributed to Hisayoshi Muraki.

14 recordsLinked to original sources

arXiv2024

Beyond Wilson? Carroll from current deformations

At extreme energies, both low and high, the spacetime symmetries of relativistic quantum field theories (QFTs) are expected to change with Galilean symmetries emerging in the very low energy domain and, as we will argue, Carrollian symmetries appearing at very high energies. The formulation of Wilsonian renormalisation group seems inadequate for handling these changes of the underlying Poincare symmetry of QFTs and it seems unlikely that these drastic changes can be seen within the realms of relativistic QFT. We show that contrary to this expectation, changes in the spacetime algebra occurs at the very edges of parameter space. In particular, we focus on the very high energy sector and show how bilinears of $U(1)$ currents added to a two dimensional (massless) scalar field theory deform the relativistic spacetime conformal algebra to conformal Carroll as the effective coupling of the deformation is dialed to infinity. We demonstrate this using both a symmetric and an antisymmetric current-current deformation for theories with multiple scalar fields. These two operators generate distinct kinds of quantum flows in the coupling space, the symmetric driven by Bogoliubov transformations and the antisymmetric by spectral flows, both leading to Carrollian CFTs at the end of the flow.

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arXiv2022

Boosting to BMS

Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, are intrinsically associated to null manifolds and in two dimensions can be obtained as an In{ö}n{ü}-Wigner contraction of the two-dimensional ($2d$) relativistic conformal algebra. Instead of performing contractions, we demonstrate in this paper how this transmutation of symmetries can be achieved by infinite boosts or degenerate linear transformations on coordinates. Taking explicit cues from the worldsheet theory of null strings, we show boosting the system is equivalent to adding a current-current deformation term to the Hamiltonian. As the strength of this deformation term reaches a critical value, the classical symmetry algebra "flows" from two copies of Virasoro to the BMS algebra. We further explore the situation where the CFT coordinates are asymmetrically transformed, and degenerate limits lead to chiral theories.

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arXiv2020

Noncommutativity in two-matrix model extension of one-dimensional topological gravity

One-dimensional topological gravity is defined as a Gaussian integral as its partition function. The Gaussian integral supplies a toy model as a simpler version of one-matrix model that is well known to provide a description of two-dimensional topological gravity. The one-dimensional topological gravity inherits an integrable hierarchy structure as with two-dimensional topological gravity, yet it is the Burgers hierarchy rather than the Korteweg--de Vries hierarchy. Making use of this fact, an extension of the one-dimensional topological gravity to an analogue of two-matrix model is investigated and the associated partition function is shown to consist of a pair of partition functions of one-dimensional topological gravity intertwined via the Moyal--Weyl product, which enables to provide an explicit formula for its free energy. The extended system shows a hierarchy structure interpreted as a noncommutative extension of the Burgers hierarchy. The relation to noncommutative U(1) gauge theory is suggested.

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arXiv2019

The null identities for boundary operators in the $(2,2p+1)$ minimal gravity

By using the matrix-model representation, we show that correlation numbers of boundary changing operators (BCO) in $(2,2p+1)$ minimal Liouville gravity satisfy some identities, which we call the null identities. These identities enable us to express the correlation numbers of BCO in terms of those of boundary preserving operators. We also discuss a physical implication of the null identities as the manifestation of the boundary interaction.

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arXiv2019

From minimal gravity to open intersection theory

We investigated the relation between the two-dimensional minimal gravity (Lee-Yang series) with boundaries and open intersection theory. It is noted that the minimal gravity with boundaries is defined in terms of boundary cosmological constant $μ_B$ and the open intersection theory in terms of boundary marked point generating parameter $s$. Based on the conjecture that the two different descriptions of the generating functions are related by the Laplace transform, we derive the compact expressions for the generating function of the intersection theory from that of the minimal gravity on a disk and on a cylinder.

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arXiv2018

Open KdV hierarchy of 2d minimal gravity of Lee-Yang series

We present the open KdV hierarchy of 2d minimal gravity of Lee-Yang series which uses the boundary cosmological constant as a flow parameter. The boundary cosmological constant is a conjugate variable to the boundary flow parameter used in the open KdV hierarchy of the intersection numbers on the moduli space of Riemann surfaces with boundaries. The two generating functions are related through the Laplace transform.

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arXiv2018

Open KdV hierarchy and minimal gravity on disk

We show that the minimal gravity of Lee-Yang series on disk is a solution to the open KdV hierarchy proposed for the intersection theory on the moduli space of Riemann surfaces with boundary.

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arXiv2018

Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry

We consider the information metric and Berry connection in the context of noncommutative matrix geometry. We propose that these objects give a new method of characterizing the fuzzy geometry of matrices. We first give formal definitions of these geometric objects and then explicitly calculate them for the well-known matrix configurations of fuzzy $S^2$ and fuzzy $S^4$. We find that the information metrics are given by the usual round metrics for both examples, while the Berry connections coincide with the configurations of the Wu-Yang monopole and the Yang monopole for fuzzy $S^2$ and fuzzy $S^4$, respectively. Then, we demonstrate that the matrix configurations of fuzzy $S^n$ $(n=2,4)$ can be understood as images of the embedding functions $S^n\rightarrow \textbf{R}^{n+1}$ under the Berezin-Toeplitz quantization map. Based on this result, we also obtain a mapping rule for the Laplacian on fuzzy $S^4$.

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arXiv2018

Commutative Geometry for Non-commutative D-branes by Tachyon Condensation

There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-abelian. We show that we can use tachyon condensation to determine the position or the shape of D0-branes uniquely as a commutative region in spacetime together with non-trivial gauge flux on it, even if the scalar fields are non-abelian. We use the idea of the so-called coherent state method developed in the field of matrix models in the context of the tachyon condensation. We investigate configurations of noncommutative D2-brane made out of D0-branes as examples. In particular, we examine a Moyal plane and a fuzzy sphere in detail, and show that whose shapes are commutative $\mathbb{R}^2$ and $S^2$, respectively, equipped with uniform magnetic flux on them. We study the physical meaning of this commutative geometry made out of matrices, and propose an interpretation in terms of K-homology.

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arXiv2018

Contravariant geometry and emergent gravity from noncommutative gauge theories

We investigate a relation of the contravariant geometry to the emergent gravity from noncommutative gauge theories. We give a refined formulation of the contravariant gravity and provide solutions to the contravariant Einstein equation. We linearize the equation around background solutions, including curved ones. A noncommutative gauge theory on the Moyal plane can be rewritten as an ordinary gauge theory on a curved background via the Seiberg-Witten map, which is known as the emergent gravity. We show that this phenomenon also occurs for a gauge theory on a noncommutative homogeneous Kähler background. We argue that the resulting geometry can be naturally described by the contravariant geometry under an identification of the fluctuation of the Poisson tensor with the field strength obtained by the Seiberg-Witten map. These results indicate that the contravariant gravity is a suitable framework for noncommutative spacetime physics.

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arXiv2018

Dual Frobenius manifolds of minimal gravity on disk

Liouville field theory approach to 2-dimensional gravity possesses the duality ($b \leftrightarrow b^{-1}$). The matrix counterpart of minimal gravity $\mathcal{M}(q,p)$ ($q<p$ co-prime) is effectively described on $A_{q-1}$ Frobenius manifold, which may exhibit a similar duality $p\leftrightarrow q$, and allow a description on $A_{p-1}$ Frobenius manifold. We have positive results from the bulk one-point and the bulk-boundary two-point correlations on disk that the dual description of the Frobenius manifold works for the unitary series $\mathcal{M}(q, q+1)$. However, for the Lee-Yang series $\mathcal{M}(2, 2q+1)$ on disk the duality is checked only partially. The main difficulty lies in the absence of a canonical description of trace in the continuum limit.

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arXiv2017

Contravariant Gravity on Poisson Manifolds and Einstein Gravity

A relation between gravity on Poisson manifolds proposed in arXiv:1508.05706 and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein-Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner.

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arXiv2016

Kähler structure in the commutative limit of matrix geometry

We consider the commutative limit of matrix geometry described by a large-$N$ sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a Kähler structure. We find an explicit relation between the Kähler structure and the matrix configurations which define the matrix geometry. We also find a relation between the matrix configurations and those obtained from the geometric quantization.

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arXiv2015

Gravity theory on Poisson manifold with $R$-flux

A novel gravity theory based on Poisson Generalized Geometry is investigated. A gravity theory on a Poisson manifold equipped with a Riemannian metric is constructed from a contravariant version of the Levi-Civita connection, which is based on the Lie algebroid of a Poisson manifold. Then, we show that in Poisson Generalized Geometry the $R$-fluxes are consistently coupled with such a gravity. An $R$-flux appears as a torsion of the corresponding connection in a similar way as an $H$-flux which appears as a torsion of the connection for- mulated in the standard Generalized Geometry. We give an analogue of the Einstein-Hilbert action coupled with an $R$-flux, and show that it is invariant under both $β$-diffeomorphisms and $β$-gauge transformations.

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