arXiv subjects

Sotaro Sugishita

Publications and source records attributed to Sotaro Sugishita.

36 records · Page 2Linked to original sources

arXiv2019

Dressed states from gauge invariance

The dressed state formalism enables us to define the infrared finite $S$-matrix for QED. In the formalism, asymptotic charged states are dressed by clouds of photons. The dressed asymptotic states are originally obtained by solving the dynamics of the asymptotic Hamiltonian in the far past or future region. However, there was an argument that the obtained dressed states are not gauge invariant. We resolve the problem by imposing a correct gauge invariant condition. We show that the dressed states can be obtained just by requiring the gauge invariance of asymptotic states. In other words, Gauss's law naturally leads to proper asymptotic states for the infrared finite $S$-matrix. We also discuss the relation between the dressed state formalism and the asymptotic symmetry for QED.

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arXiv2018

Deep Learning and Holographic QCD

We apply the relation between deep learning (DL) and the AdS/CFT correspondence to a holographic model of QCD. Using a lattice QCD data of the chiral condensate at a finite temperature as our training data, the deep learning procedure holographically determines an emergent bulk metric as neural network weights. The emergent bulk metric is found to have both a black hole horizon and a finite-height IR wall, so shares both the confining and deconfining phases, signaling the cross-over thermal phase transition of QCD. In fact, a quark antiquark potential holographically calculated by the emergent bulk metric turns out to possess both the linear confining part and the Debye screening part, as is often observed in lattice QCD. From this we argue the discrepancy between the chiral symmetry breaking and the quark confinement in the holographic QCD. The DL method is shown to provide a novel data-driven holographic modeling of QCD, and sheds light on the mechanism of emergence of the bulk geometries in the AdS/CFT correspondence.

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arXiv2018

Notes on the gravitational, electromagnetic and axion memory effects

We investigate the memory effects associated with the kicks of particles. Recently, the equivalence between the memory effect and soft theorem has been established. By computing the memory effect from the radiation solutions, we explicitly confirm that, in addition to the leading piece, the subleading and subsubleading soft theorems are equivalent to the subleading and subsubleading memory effects, respectively. It is known that the memory effects can be probed by the displacements or kicks of the test particles. We point out that the these memory effects are also probed by the permanent change of the direction of the spin. We also show that the axion memory effect, recently proposed by the current authors, can be detected as the change of the spin of the test particle. We discuss that if we consider the magnetic monopole as an external particle, the parity-odd electromagnetic memory appears.

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arXiv2018

Conservation Laws from Asymptotic Symmetry and Subleading Charges in QED

We present several results on memory effects, asymptotic symmetry and soft theorems in massive QED. We first clarify in what sense the memory effects are interpreted as the charge conservation of the large gauge transformations, and derive the leading and subleading memory effects in classical electromagnetism. We also show that the sub-subleading charges are not conserved without including contributions from the spacelike infinity. Next, we study QED in the BRST formalism and show that parts of large gauge transformations are physical symmetries by justifying that they are not gauge redundancies. Finally, we obtain the expression of charges associated with the subleading soft photon theorem in massive scalar QED.

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arXiv2018

Thoughts on Holographic Complexity and its Basis-dependence

In this paper, we argue that holographic complexity should be a basis-dependent quantity. Computational complexity of a state is defined as a minimum number of gates required to obtain that state from the reference state. Due to this minimality, it satisfies the triangle inequality, and can be regarded as a (discrete version of) distance in the Hilbert space. However, we show a no-go theorem that any basis-independent distance cannot reproduce the behavior of the holographic complexity. Therefore, if holographic complexity is dual to a distance in the Hilbert space, it should be basis-dependent, i.e., it is not invariant under a change of the basis of the Hilbert space.

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arXiv2018

Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game -

Quantum complexity is conjectured to probe inside of black hole horizons (or wormhole) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for generic Abelian pure gauge theories. For this purpose, we discretize $U(1)$ gauge group as $\mathbf{Z}_N$ and also continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories, and evaluate time evolutions of the complexities explicitly. We find that for a generic class of diagonal Hamiltonians to achieve a large complexity $\sim \exp(\mbox{entropy})$, which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.

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arXiv2018

Deep Learning and AdS/CFT

We present a deep neural network representation of the AdS/CFT correspondence, and demonstrate the emergence of the bulk metric function via the learning process for given data sets of response in boundary quantum field theories. The emergent radial direction of the bulk is identified with the depth of the layers, and the network itself is interpreted as a bulk geometry. Our network provides a data-driven holographic modeling of strongly coupled systems. With a scalar $ϕ^4$ theory with unknown mass and coupling, in unknown curved spacetime with a black hole horizon, we demonstrate our deep learning (DL) framework can determine them which fit given response data. First, we show that, from boundary data generated by the AdS Schwarzschild spacetime, our network can reproduce the metric. Second, we demonstrate that our network with experimental data as an input can determine the bulk metric, the mass and the quadratic coupling of the holographic model. As an example we use the experimental data of magnetic response of a strongly correlated material Sm$_{0.6}$Sr$_{0.4}$MnO$_3$. This AdS/DL correspondence not only enables gravity modeling of strongly correlated systems, but also sheds light on a hidden mechanism of the emerging space in both AdS and DL.

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arXiv2017

Entanglement entropy for free scalar fields in AdS

We compute entanglement entropy for free massive scalar fields in anti-de Sitter (AdS) space. The entangling surface is a minimal surface whose boundary is a sphere at the boundary of AdS. The entropy can be evaluated from the thermal free energy of the fields on a topological black hole by using the replica method. In odd-dimensional AdS, exact expressions of the Renyi entropy $S_n$ are obtained for arbitrary $n$. We also evaluate 1-loop corrections coming from the scalar fields to holographic entanglement entropy. Applying the results, we compute the leading difference of entanglement entropy between two holographic CFTs related by a renormalization group flow triggered by a double trace deformation. The difference is proportional to the shift of a central charge under the flow.

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arXiv2017

Soft pion theorem, asymptotic symmetry and new memory effect

It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the $S$-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.

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arXiv2017

On the Time Dependence of Holographic Complexity

We evaluate the full time dependence of holographic complexity in various eternal black hole backgrounds using both the complexity=action (CA) and the complexity=volume (CV) conjectures. We conclude using the CV conjecture that the rate of change of complexity is a monotonically increasing function of time, which saturates from below to a positive constant in the late time limit. Using the CA conjecture for uncharged black holes, the holographic complexity remains constant for an initial period, then briefly decreases but quickly begins to increase. As observed previously, at late times, the rate of growth of the complexity approaches a constant, which may be associated with Lloyd's bound on the rate of computation. However, we find that this late time limit is approached from above, thus violating the bound. Adding a charge to the eternal black holes washes out the early time behaviour, i.e., complexity immediately begins increasing with sufficient charge, but the late time behaviour is essentially the same as in the neutral case. We also evaluate the complexity of formation for charged black holes and find that it is divergent for extremal black holes, implying that the states at finite chemical potential and zero temperature are infinitely more complex than their finite temperature counterparts.

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arXiv2016

Triangle-hinge models for unoriented membranes

Triangle-hinge models [arXiv:1503.08812] are introduced to describe worldvolume dynamics of membranes. The Feynman diagrams consist of triangles glued together along hinges and can be restricted to tetrahedral decompositions in a large N limit. In this paper, after clarifying that all the tetrahedra resulting in the original models are orientable, we define a version of triangle-hinge models that can describe the dynamics of unoriented membranes. By regarding each triangle as representing a propagation of an open membrane of disk topology, we introduce a local worldvolume parity transformation which inverts the orientation of triangle, and define unoriented triangle-hinge models by gauging the transformation. Unlike two-dimensional cases, this local transformation generally relates a manifold to a nonmanifold, but still is a well-defined manipulation among tetrahedral decompositions. We further show that matter fields can be introduced in the same way as in the original oriented models. In particular, the models will describe unoriented membranes in a target spacetime by taking matter fields to be the target space coordinates.

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arXiv2016

Matter fields in triangle-hinge models

The worldvolume theory of membrane is mathematically equivalent to three-dimensional quantum gravity coupled to matter fields corresponding to the target space coordinates of embedded membrane. In a recent paper [arXiv:1503.08812] a new class of models are introduced that generate three-dimensional random volumes, where the Boltzmann weight of each configuration is given by the product of values assigned to the triangles and the hinges. These triangle-hinge models describe three-dimensional pure gravity and are characterized by semisimple associative algebras. In this paper, we introduce matter degrees of freedom to the models by coloring simplices in a way that they have local interactions. This is achieved simply by extending the associative algebras of the original triangle-hinge models, and the profile of matter field is specified by the set of colors and the form of interactions. The dynamics of a membrane in $D$-dimensional spacetime can then be described by taking the set of colors to be $\mathbb{R}^D$. By taking another set of colors, we can also realize three-dimensional quantum gravity coupled to the Ising model, the $q$-state Potts models or the RSOS models. One can actually assign colors to simplices of any dimensions (tetrahedra, triangles, edges and vertices), and three-dimensional colored tensor models can be realized as triangle-hinge models by coloring tetrahedra, triangles and edges at a time.

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arXiv2015

Random volumes from matrices

We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by semisimple associative algebras A. Although most of the diagrams represent configurations which are not manifolds, we show that the set of possible diagrams can be drastically reduced such that only (and all of the) three-dimensional manifolds with tetrahedral decompositions appear, by introducing a color structure and taking an appropriate large N limit. We examine the analytic properties when A is a matrix ring or a group ring, and show that the models with matrix ring have a novel strong-weak duality which interchanges the roles of triangles and hinges. We also give a brief comment on the relationship of our models with the colored tensor models.

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arXiv2015

Ramond-Ramond couplings of D-branes

Applying supersymmetric localization for superstring worldsheet theory with N=(1,1) supersymmetries on a cylinder and with arbitrary boundary interactions, we find the most general formula for the Ramond-Ramond (RR) coupling of D-branes. We allow all massive excitations of open superstrings, and find that only a finite number of them can contribute to the formula. The formula is written by Quillen's superconnection which includes higher form gauge fields, and the resultant general Chern-Simons terms are consistent with RR charge quantization. Applying the formula to boundary string field theory of a BPS D9-brane or a D9-antiD9 brane system, we find that any D9-brane creation via massive mode condensation is impossible.

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arXiv2014

Holographic Holes in Higher Dimensions

We extend the holographic construction from AdS3 to higher dimensions. In particular, we show that the Bekenstein-Hawking entropy of codimension-two surfaces in the bulk with planar symmetry can be evaluated in terms of the 'differential entropy' in the boundary theory. The differential entropy is a certain quantity constructed from the entanglement entropies associated with a family of regions covering a Cauchy surface in the boundary geometry. We demonstrate that a similar construction based on causal holographic information fails in higher dimensions, as it typically yields divergent results. We also show that our construction extends to holographic backgrounds other than AdS spacetime and can accommodate Lovelock theories of higher curvature gravity.

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arXiv2014

Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space

We derive the master equation that completely determines the time evolution of the density matrix of the Unruh-DeWitt detector in an arbitrary background geometry. We apply the equation to reveal a nonequilibrium thermodynamic character of de Sitter space. This generalizes an earlier study on the thermodynamic property of the Bunch-Davies vacuum that an Unruh-DeWitt detector staying in the Poincare patch and interacting with a scalar field in the Bunch-Davies vacuum behaves as if it is in a thermal bath of finite temperature. In this paper, instead of the Bunch-Davies vacuum, we consider a class of initial states of scalar field, for which the detector behaves as if it is in a medium that is not in thermodynamic equilibrium and that undergoes a relaxation to the equilibrium corresponding to the Bunch-Davies vacuum. We give a prescription for calculating the relaxation times of the nonequilibrium processes. We particularly show that, when the initial state of the scalar field is the instantaneous ground state at a finite past, the relaxation time is always given by a universal value of half the curvature radius of de Sitter space. We expect that the relaxation time gives a nonequilibrium thermodynamic quantity intrinsic to de Sitter space.

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arXiv2013

Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries

We construct supersymmetric gauge theories on some curved manifolds with boundaries. Our examples include a part of three-sphere and a part of two-sphere. We concentrate on Dirichlet boundary conditions. For these theories on the manifolds with the boundaries, we compute the partition functions and the Wilson loops exactly using the localization technique.

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arXiv2013

Propagators in de Sitter space

In a spacetime with no global timelike Killing vector, we do not have a natural choice for the vacuum state of matter fields, leading to an ambiguity in defining the Feynman propagators. In this paper, taking the vacuum state to be the instantaneous ground state of the Hamiltonian at each moment, we develop a method for calculating wave functions associated with the vacuum and the corresponding in-in and in-out propagators. We apply this method to free scalar field theory in de Sitter space and obtain de Sitter invariant propagators in various coordinate patches. We show that the in-out propagator in the Poincare patch has a finite massless limit in a de Sitter invariant form. We argue and numerically check that our in-out propagators agree with those obtained by a path integral with the standard iεprescription, and identify the condition on a foliation of spacetime under which such coincidence can happen for the foliation. We also show that the in-out propagators satisfy Polyakov's composition law. Several applications of our framework are also discussed.

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