arXiv subjects

Yasuaki Hikida

Publications and source records attributed to Yasuaki Hikida.

At least 37 records · Page 2Linked to original sources

arXiv2020

Correlation functions of symmetric orbifold from AdS$_3$ string theory

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The result should be an important ingredient for deriving AdS$_3$/CFT$_2$ correspondence with tensionless superstrings to all orders in string perturbation theory.

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arXiv2019

Rectangular W-(super)algebras and their representations

We study W-algebras obtained by quantum Hamiltonian reduction of $sl(Mn)$ associated to the $sl(2)$ embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued fields. In our previous work, we examined the basic properties of the W-algebra and claimed that the algebra can be realized as the symmetry of Grassmannian-like coset even with finite central charge based on a proposal of holography. In this paper, we extend the analysis in the following ways. First, we compute the operator product expansions among low spin generators removing the restriction of $n = 2$. Second, we investigate the degenerate representations in several ways, and see the relations to the coset spectrum and the conical defect geometry of the higher spin gravity. For these analyses, we mainly set $M=n=2$. Finally, we extend the previous analysis by introducing $\mathcal{N}=2$ supersymmetry.

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arXiv2019

Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs

We examine rectangular W-algebras with $so(M)$ or $sp(2M)$ symmetry, which can be realized as the asymptotic symmetry of higher spin gravities with restricted matrix extensions. We compute the central charges of the algebras and the levels of $so(M)$ or $sp(2M)$ affine subalgebras by applying the Hamiltonian reductions of $so$ or $sp$ type Lie algebras. For simple cases with generators of spin up to two, we obtain their operator product expansions by requiring the associativity. We further claim that the W-algebras can be realized as the symmetry algebras of dual coset CFTs and provide several strong supports. The analysis can be regarded as a check of extended higher spin holographies including full quantum corrections. We also extend the analysis by introducing $\mathcal{N}=1$ supersymmetry.

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arXiv2019

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs

We analyze the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued fields, which is given by rectangular W-algebras with su$(M)$ symmetry. The matrix valued extension is expected to be useful for the relation between higher spin gravity and string theory. With the truncation of spin as $s=2,3,\ldots , n$, we evaluate the central charge $c$ of the algebra and the level $k$ of the affine currents with finite $c,k$. For the simplest case with $n=2$, we obtain the operator product expansions among generators by requiring their associativity. We conjecture that the symmetry is the same as that of Grassmannian-like coset based on our proposal of higher spin holography. Comparing $c,k$ from the both theories, we obtain the map of parameters. We explicitly construct low spin generators from the coset theory, and, in particular, we reproduce the operator product expansions of the rectangular W-algebra for $n=2$. We interpret the map of parameters by decomposing the algebra in the coset description.

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arXiv2018

Superconformal blocks from Wilson lines with loop corrections

We compute the $\mathcal{N}=1$ superconformal blocks from the networks of open Wilson lines in the $\text{osp}(1|2)$ Chern-Simons theory in the expansion of large central charge $c$. We first reproduce the $1/c$ correction of conformal weight from an open Wilson line by adopting the regularization prescription developed in our previous works. We then obtain the closed form expressions of superconformal blocks including $1/c$ corrections, which were not available before. We also examine heavy operators corresponding to supersymmetric conical spaces, and the geometry is quantized by utilizing the coadjoint orbits of the super Virasoro group. Superconformal blocks involving these operators are also examined.

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arXiv2018

ETH and Modular Invariance of 2D CFTs

We study properties of heavy-light-heavy three-point functions in two-dimensional CFTs by using the modular invariance of two-point functions on a torus. We show that our result is non-trivially consistent with the condition of ETH (Eigenstate Thermalization Hypothesis). We also study the open-closed duality of cylinder amplitudes and derive behaviors of disk one-point functions.

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arXiv2018

Conformal blocks from Wilson lines with loop corrections

We compute the conformal blocks of the Virasoro minimal model or its W$_N$ extension with large central charge from Wilson line networks in a Chern-Simons theory including loop corrections. In our previous work, we offered a prescription to regularize divergences from loops attached to Wilson lines. In this paper, we generalize our method with the prescription by dealing with more general operators for $N=3$ and apply it to the identity W$_3$ block. We further compute general light-light blocks and heavy-light correlators for $N=2$ with the Wilson line method and compare the results with known ones obtained using a different prescription. We briefly discuss general W$_3$ blocks.

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arXiv2017

Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections

We study the correlators of the 2d W_N minimal model in the semiclassical regime with large central charge from bulk viewpoint by utilizing open Wilson lines in sl(N) Chern-Simons gauge theory. We extend previous works for the tree level of bulk theory to incorporate loop corrections in this paper. We offer a way to regularize divergences associated with loop diagrams such that three point functions with two scalars and a higher spin current agree with the values fixed by the boundary W_N symmetry. With the prescription, we reproduce the conformal weight of the operator corresponding to a bulk scalar up to the two loop order for explicit examples with N=2,3.

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arXiv2017

Three point functions in higher spin AdS_3 holography with 1/N corrections

We examine three point functions with two scalar operators and a higher spin current in 2d W_N minimal model to the next non-trivial order in 1/N expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and 1/N corrections should be interpreted as quantum effects in the dual gravity theory. We develop a simple and systematic method to obtain three point functions by decomposing four point functions of scalar operators with Virasoro conformal blocks. Applying the method, we reproduce known results at the leading order in 1/N and obtain new ones at the next leading order. As confirmation, we check that our results satisfy relations among three point functions conjectured before.

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arXiv2017

Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry

We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the masses of higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory.

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arXiv2017

Anomalous dimensions of higher spin currents in large N CFTs

We examine anomalous dimensions of higher spin currents in the critical O(N) scalar model and the Gross-Neveu model in arbitrary d dimensions. These two models are proposed to be dual to the type A and type B Vasiliev theories, respectively. We reproduce the known results on the anomalous dimensions to the leading order in 1/N by using conformal perturbation theory. This work can be regarded as an extension of previous work on the critical O(N) scalars in 3 dimensions, where it was shown that the bulk computation for the masses of higher spin fields on AdS_4 can be mapped to the boundary one in conformal perturbation theory. The anomalous dimensions of the both theories agree with each other up to an overall factor depending only on d, and we discuss the coincidence for d=3 by utilizing N=2 supersymmetry.

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arXiv2016

The masses of higher spin fields on AdS_4 and conformal perturbation theory

We study the breaking of gauge symmetry for higher spin theory on AdS_4 dual to the 3d critical O(N) vector model. It was argued that the breaking is due to the change of boundary condition for a scalar field through a loop effect and the Goldstone modes are bound states of a scalar field and higher spin field. The masses of higher spin fields were obtained from the anomalous dimensions of dual currents at the leading order in 1/N, and we reproduce them from the O(N) vector model in the conformal perturbation theory. The anomalous dimensions can be computed from the bulk theory using Witten diagrams, and we show that the bulk computation reduces to the boundary one in the conformal perturbation theory. With this fact our computation provides an additional support for the bulk interpretation.

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arXiv2015

Higgs phenomenon for higher spin fields on AdS_3

In a previous work, a marginal deformation of 2d coset type model with N=3 superconformal symmetry was studied, and it was interpreted as a change of boundary conditions for bulk fields in the dual higher spin theory. The deformation breaks generic higher spin gauge symmetry, and the generated mass of a spin 2 field was computed. The deformation might be related to the introduction of finite string tension in a superstring theory. In this paper, we extend the analysis and compute the masses of generic higher spin fields at the leading order of 1/c (c is the CFT central charge) but at the full order of the deformation parameter. We find that the masses are not generated for so(3)_R singlet higher spin fields at this order and the spectrum is the Regge-like one for so(3)_R triplet higher spin-charged fields.

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arXiv2015

Correspondences between WZNW models and CFTs with W-algebra symmetry

We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W-algebra symmetry. The symmetries of the theories involved in these correspondences are related by the Drinfeld-Sokolov reduction of Lie algebras to W-algebras. The W-algebras considered in this paper are the Bershadsky-Polyakov algebra for sl(3) and the quasi-superconformal algebra for generic sl(N|M). The quantum W-algebras obtained from affine sl(N) are constructed using embeddings of sl(2) into sl(N), and these can in turn be characterized by partitions of N. The above cases correspond to \underline{N+2} = \underline{2} + N \underline{1} and its supergroup extension. Finally, sl(2N) and the correspondence corresponding to \underline{2N} = N \underline{2} is also analyzed.

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arXiv2015

Marginal deformations and the Higgs phenomenon in higher spin AdS_3 holography

Recently, a 2d coset model with N=3 superconformal symmetry was proposed to be holographic dual to a higher spin supergravity on AdS_3 and the relation to superstring theory was discussed. However, away from the tensionless limit, there is no higher spin symmetry and the higher spin states are massive. In this paper, we examine the deformations of the coset model which preserve N=3 superconformal symmetry, but break generic higher spin symmetry. We focus on double-trace type deformations which are dual to changes of boundary conditions for the bulk matter fields. In the bulk theory, the symmetry breaking will generate mass for the higher spin fields. As a concrete example, we compute the Higgs mass of a spin 2 field both from the bulk and the boundary theory.

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arXiv2015

Higher spin AdS_3 holography and superstring theory

It has been believed for a long time that the tensionless limit of superstring theory can be described by a higher spin gauge theory. Recently, a concrete realization of this idea was proposed via 3d Aharony-Bergman-Jafferis (ABJ) theory with the help of holographic duality. In this note we review our work on finding a similar relation involving 2d coset type models. We start by proposing and examining holographic dualities between 3d higher spin gauge theories with matrix valued fields and the large N limit of 2d coset type models. After that we discuss possible relations to superstring theory with emphasis on the role of the matrix form of the higher spin fields and the extended supersymmetry.

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arXiv2014

Higher spin AdS_3 holography with extended supersymmetry

We propose a holographic duality between a higher spin AdS_3 gravity with so(p) extended supersymmetry and a large N limit of a 2-dimensional Grassmannian-like model with a specific critical level k=N and a non-diagonal modular invariant. As evidence, we show the match of one-loop partition functions. Moreover, we construct symmetry generators of the coset model for low spins which are dual to gauge fields in the supergravity. Further, we discuss a possible relation to superstring theory by noticing an N=3 supersymmetry of critical level model at finite k,N. In particular, we examine BPS states and marginal deformations. Inspired by the supergravity side, we also propose and test another large N CFT dual obtained as a Z_2 automorphism truncation of a similar coset model, but at a non-critical level.

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arXiv2014

Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov W^(2)_n-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n=2 and n=4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k+n=(n+1)/(n-1). At these points, the W^(2)_n-algebra is nothing but a compactified free boson. This family of W-algebras admits an 't Hooft limit that is similar to the original minimal model 't Hooft limit. Further, in the case of n=4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product.

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