arXiv subjects

Shigenori Seki

Publications and source records attributed to Shigenori Seki.

At least 19 recordsLinked to original sources

arXiv2026

Vertex Operators in Superstring Theory from Integral Forms and Descent Equations

We develop a geometric formulation of vertex operators in superstring theory based on integral forms on super Riemann surfaces. Starting from the integrated NS-NS vertex operator, we derive descent equations that relate operators with different ghost and picture numbers. A key result is a correspondence between supergeometric objects and ghost superfields, in which the one-form $dz-θdθ$ and the even differential $dθ$ are identified with the ghost superfield and its superderivative. This provides a geometric realization of the superghost structure. We further extend the construction by incorporating inverse picture-changing operators, which generate new descent sequences across different picture sectors. We also introduce a superfield construction of higher-ghost-number operators, for which additional terms are required compared to the bosonic case. All operators are organized into a universal descent structure and are well-defined in BRST cohomology.

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arXiv2026

Entanglement in Elastic and Inelastic Two-particle Scatterings at High Energy

We study the entanglement produced in transverse momentum by two-particle scattering at high energy. Employing the S-matrix framework for the derivation of reduced density matrices, we formulate the entanglement entropy for an inelastic scattering as well as an elastic one. We display the formulas of the entanglement entropy in terms of two-body cross sections. We also derive the entanglement density as a function of the transverse momentum. As an application, we then focus on both forward elastic ($pn \to pn$) and inelastic ($pn \to np$) channels scattering allowing for a fruitful comparison of the two reactions with the same proton-neutron content. We evaluate the elastic and inelastic entanglement entropy by using known parameterizations of experimental data for neutron-proton reactions. Comparing those entanglement entropies, we observe that the inelastic scattering produces more overall entanglement than the elastic one in the $pn$ sector.

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arXiv2024

Closed string vertex operators with various ghost number

We construct closed string vertex operators with various ghost numbers in addition to the conventional ones, using the Faddeev-Popov procedure for the gauge fixing of the conformal Killing group, from matter primary fields. We find that these operators give solutions to the descent equations in the framework of the BRST formalism. Similarly, we also construct solutions to the descent equations for the dilaton vertex operator with the Lorentz covariant form. Using the unintegrated vertex operator of the dilaton with the ghost number three, we obtain the correct result of the tadpole amplitude on the disk, including a non-zero contribution from a BRST exact term which comes from a conformal transformation.

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arXiv2024

Two-point closed string amplitudes in the BRST formalism

Two-point tree-level amplitudes in bosonic closed string theory are described by a correlation function within the BRST formalism, which respects manifest Lorentz and conformal invariance. In the derivation of the two-point amplitudes, we use the mostly BRST exact operator, which has been introduced for two-point open string amplitudes, and a closed string vertex with ghost number three, which has been explored in our recent work, in addition to the conventional one.

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arXiv2021

The Veneziano Amplitude via Mostly BRST Exact Operator

The Veneziano amplitude is derived from fixing one degree of freedom of $PSL(2,\mathbb{R})$ symmetry by the insertion of a mostly BRST exact operator. Evaluating the five-point function which consists of four open string tachyons and this gauge fixing operator, we find it equals the Veneziano amplitude up to a sign factor. The sign factor is interpreted as a signed intersection number.The result implies that the mostly BRST exact operator, which is originally used to provide two-point string amplitudes, correctly fixes the $PSL(2,\mathbb{R})$ gauge symmetry for general amplitudes. We conjecture an expression for general $n$-point tree amplitudes with an insertion of this gauge fixing operator.

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arXiv2021

Reduction of Open String Amplitudes by Mostly BRST Exact Operators

We study two and three-point tree-level amplitudes of open strings. These amplitudes are reduced from higher-point correlation functions by using mostly BRST exact operators for gauge fixing. For simplicity, we focus on an open string tachyon. The two-point amplitude of open string tachyons is reduced from a three-point function of two tachyon vertex operators and one mostly BRST exact operator. Similarly the three-point amplitude is from a four-point function of three tachyon vertex operators and one mostly BRST exact operator. One can also obtain the two-point amplitude from the four-point function of two tachyon vertex operators and two mostly BRST exact operators. In these derivation from four-point functions, moduli integrals are significant. We discuss the overall signs of amplitudes which are indefinite in this formalism.

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arXiv2019

Two-point String Amplitudes Revisited by Operator Formalism

So far we have considered that a two-point string amplitude vanishes due to the infinite volume of residual gauge symmetry. However recently Erbin-Maldacena-Skliros have suggested that the two-point amplitude can have non-zero value, because one can cancel the infinite volume by the infinity coming from on-shell energy conservation. They derived the two-point function by Fadeev-Popov method. In this paper we revisit this two-point string amplitude in the operator formalism. We find the mostly BRST exact operator which yields non-zero two-point amplitudes.

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arXiv2019

Evaluation of Entanglement Entropy in High Energy Elastic Scattering

Entanglement of the two scattered particles is expected to occur in elastic collisions, even at high energy where they are in competition with inelastic ones. We study how to evaluate quantitatively the corresponding entanglement entropy $S_{\rm EE}.$ For this sake, we regularize the divergences occurring in the formal derivation of $S_{\rm EE}$ using a regularization procedure acting on the two-particle Hilbert space of final states. A quantitative application is performed in proton-proton collisions at collider energies, comparing the results of $S_{\rm EE}$ with two different cut-offs and with a volume-regularization obtained by a prescription fixing the finite two-body Hilbert space volume. A significant entanglement is found which persists even at the highest available energies.

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arXiv2016

Entanglement Entropy of Scattering Particles

We study the entanglement entropy between the two outgoing particles in an elastic scattering process. It is formulated within an S-matrix formalism using the partial wave expansion of two-body states, which plays a significant role in our computation. As a result, we obtain a novel formula that expresses the entanglement entropy in a high energy scattering by the use of physical observables, namely the elastic and total cross sections and a physical bound on the impact parameter range, related to the elastic differential cross-section.

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arXiv2015

Variation of Entanglement Entropy in Scattering Process

In a scattering process, the final state is determined by an initial state and an S-matrix. We focus on two-particle scattering processes and consider the entanglement between these particles. For two types initial states; i.e., an unentangled state and an entangled one, we calculate perturbatively the change of entanglement entropy from the initial state to the final one. Then we show a few examples in a field theory and in quantum mechanics.

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arXiv2014

EPR = ER and Scattering Amplitude as Entanglement Entropy Change

We study the causal structure of the minimal surface of the four-gluon scattering, and find a world-sheet wormhole parametrized by Mandelstam variables, thereby demonstrate the EPR = ER relation for gluon scattering. We also propose that scattering amplitude is the change of the entanglement entropy by generalizing the holographic entanglement entropy of Ryu-Takayanagi to the case where two regions are divided in space-time.

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arXiv2013

A New Model of Holographic QCD and Chiral Condensate in Dense Matter

We consider the model of holographic QCD with asymptotic freedom and gluon condensation in its vacuum. It consists of the color D4-branes and D0-branes as a background and the flavor D8-branes as a probe. By taking a specific field theory limit, the effective coupling decreases to vanish in UV region. We then introduce the uniformly distributed baryons in terms of the baryon vertices and study the density dependence of chiral condensate, which is evaluated using the worldsheet instanton method. In the confined phase, the chiral condensate as a function of density monotonically decreases in high baryon density. Such behavior is in agreement with the expectation, while in extremely low density it increases. We attribute this anomaly to the incorrect approximation of uniformity in very low density. In the deconfined phase the chiral condensate monotonically decreases in the whole region of density.

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arXiv2012

Chiral Condensate in Holographic QCD with Baryon Density

We consider the chiral condensate in the baryonic dense medium using the generalized Sakai-Sugimoto model. It is defined as the vacuum expectation value of open Wilson line that is proposed to be calculated by use of the area of world-sheet instanton. We evaluate it in confined as well as deconfined phase. In both phases, the chiral condensate has a minimum as a function of baryon density. In the deconfined phase, taking into account the chiral symmetry restoration, we classify the behavior of chiral condensate into three types. One can set the parameter of the theory such that the results, in low but sufficiently higher density, is in agreement with the expectation from QCD.

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arXiv2012

Eikonal Approach to N=4 SYM Regge Amplitudes in the AdS/CFT Correspondence

The high-energy behavior of N=4 SYM elastic amplitudes at strong coupling is studied by means of the AdS/CFT correspondence. We consider the eikonal method proposed by Janik and one of the authors, where the relevant minimal surface is a "generalized helicoid" in hyperbolic space ("Euclidean AdS_5"), from which the physical amplitude is obtained after an appropriate analytic continuation. We then compare our results with those obtained, using a minimal surface in AdS_5 momentum space, by Alday and Maldacena for gluon-gluon scattering, and by Barnes and Vaman for quark-quark scattering ("Alday-Maldacena approach"). Exploiting a conformal transformation, we show that the eikonal amplitudes are dominated by the Euclidean version of the cusp contribution found in the Alday-Maldacena approach. The amplitudes in the two approaches are of Regge type at high-energy and with the same logarithmic Regge trajectory independently of the kind of colliding particles, in agreement with the expected universality of Regge trajectories.

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arXiv2010

Intersecting D4-branes Model of Holographic QCD and Tachyon Condensation

We consider the intersecting D4-brane and anti-D4-brane model of holographic QCD, motivated by the model that has recently been suggested by Van Raamsdonk and Whyte. We analyze such D4-branes by the use of the action with a bi-fundamental ``tachyon'' field, so that we find the classical solutions describing the intersecting D4-branes and the U-shaped D4-branes. We show that the ``tachyon'' field in the bulk theory provides a current quark mass and a quark condensate to the dual gauge theory and that the lowest modes of mesons obtain mass via tachyon condensation. Then evaluating the properties of a pion, one can reproduce Gell-Mann-Oakes-Renner relation.

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arXiv2009

Comments on Baryons in Holographic QCD

We generalize the description of baryons as instantons of Sakai-Sugimoto model to the case where the flavor branes are non-anti-podal. The later corresponds to quarks with a "string endpoint mass". We show that the baryon vertex is located on the flavor branes and hence the generalized baryons also associate with instantons. We calculate the baryon mass spectra, the isoscalar and axial mean square radii, the isoscalar and isovector magnetic moments and the axial coupling as a function of the mass scale M_{KK} and the location ζof the tip of U-shaped flavor D8-branes. We determine the values of M_{KK} and ζfrom a best fit comparison with the experimental data. The later comes out to be in a forbidden region, which may indicate that the incorporation of baryons in Sakai-Sugimoto model has to be modified. We discuss the analogous baryons in a non-critical gravity model. A brief comment on the single flavor case (N_f=1) is also made.

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arXiv2007

Quark mass and condensate in HQCD

We extend the Sakai-Sugimoto holographic model of QCD (HQCD) by including the scalar bi-fundamental "tachyon" field in the 8-brane-anti-8-brane probe theory. We show that this field is responsible both for the spontaneous breaking of the chiral symmetry, and for the generation of (current algebra) quark masses, from the point of view of the bulk theory. As a by-product we show how this leads to the Gell-Mann- Oakes-Renner relation for the pion mass.

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arXiv2006

Cosmological Constant Probing Shape Moduli through Large Extra Dimensions

We consider compactification of extra dimensions and numerically calculate Casimir energy which is provided by the mass of Kaluza-Klein modes. For the extra space we consider a torus with shape moduli and show that the corresponding vacuum energy is represented as a function of the moduli parameter of the extra dimensions. By assuming that the Casimir energy may be identified with cosmological constant, we evaluate the size of extra dimensions in terms of the recent data given by the WMAP observation. We suggest that the observed cosmological constant may probe the shape moduli of the extra space by the study of the Casimir energy of the compactified extra dimensions.

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