arXiv subjects

Takahiro Uetoko

Publications and source records attributed to Takahiro Uetoko.

14 recordsLinked to original sources

arXiv2024

The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach

We determine the complex geometries dual to the semi-classical saddles in three-dimensional gravity with positive or negative cosmological constant. We examine the semi-classical saddles in Liouville field theory and interpret them in terms of gravity theory. For this, we describe the gravity theory by Chern Simons theory and classify the possible saddles based on homotopy group argument. We further realize the semi-classical saddles using the mini-superspace model of quantum gravity and explicitly determine the integral contour. In the case of positive cosmological constant, we recovered the geometry used for no-boundary proposal of Hartle and Hawking. In the case of negative cosmological constant, the geometry can be identified with Euclidean anti-de Sitter space attached with imaginary radius spheres. The geometry should be unphysical and several arguments on this issue are provided. Partial results were already presented in our earlier letter, and more detailed derivations and explanations on the results are given along with additional results. In particular, we reproduce the classical Liouville action from the Chern-Simons formulation of dual gravity theory.

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arXiv2024

Semi-classical saddles of three-dimensional gravity via holography

We find out the complex geometries corresponding to the semi-classical saddles of threedimensional quantum gravity by making use of the known results of dual conformal field theory (CFT), which is effectively given by Liouville field theory. We examine both the cases with positive and negative cosmological constants. We determine the set of semi-classical saddles to choose from the homotopy argument in the Chern-Simons formulation combined with CFT results and provide strong supports from the mini-superspace approach to the quantum gravity. For the case of positive cosmological constant, partial results were already obtained in our previous works, and they are consistent with the current ones. For the case of negative cosmological constant, we identify the geometry corresponding a semi-classical saddle with three-dimensional Euclidean anti-de Sitter space dressed with imaginary radius three-dimensional spheres. The geometry is generically unphysical, but we argue that the fact itself does not lead to any problems.

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arXiv2023

Complex saddles of Chern-Simons gravity and dS$_3$/CFT$_2$ correspondence

We examine the black hole solutions of dS$_3$ gravity by applying the explicit dS$_3$/CFT$_2$ correspondence. The gravity theory is described by Chern-Simons theory with complex gauge group SL$(2,\mathbb{C})$, and the complexified theory is known to have too many saddle points. We determine the set of "allowable geometry" from dual CFT correlators. Concretely, we classify the possible complex solutions corresponding to dS$_3$ black holes from Liouville two-point functions. We extend the analysis to Liouville multi-point functions and among others we study geometry corresponding to two linked Wilson loops on $S^3$ by the monodromy matrix of Liouville four-point function. Some parts of the results were presented in a previous letter but here they are explained in more details and extended in various ways. In particular, we generalize the results to the case with higher-spin gravity by focusing the effects of higher-spin charges.

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arXiv2023

Complex saddles of three-dimensional de Sitter gravity via holography

We determine complex saddles of three-dimensional gravity with a positive cosmological constant by applying the recently proposed holography. It is sometimes useful to consider a complexified metric to study quantum gravity as in the case of the no-boundary proposal by Hartle and Hawking. However, there would be too many saddles for complexified gravity, and we should determine which saddles to take. We describe the gravity theory by three-dimensional SL$(2,\mathbb{C})$ Chern-Simons theory. At the leading order in the Newton constant, its holographic dual is given by Liouville theory with a large imaginary central charge. We examine geometry with a conical defect, called a de Sitter black hole, from a Liouville two-point function. We also consider geometry with two conical defects, whose saddles are determined by the monodromy matrix of Liouville four-point function. Utilizing Chern-Simons description, we extend the similar analysis to the case with higher-spin gravity.

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arXiv2021

Chern-Simons Gravity Dual of BCFT

In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

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arXiv2020

Argyres-Douglas Theories, S-duality and AGT Correspondence

We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional N=2 U(2) gauge theories coupled to (A_1,D_{2n}) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to the case of U(2) gauge group, which requires us to define irregular states of the direct sum of Virasoro and Heisenberg algebras. Using our formula, one can evaluate the contribution of the (A_1,D_{2n}) theory at each fixed point on the U(2) instanton moduli space. As an application, we evaluate the instanton partition function of the (A_3,A_3) theory to find it in a peculiar relation to that of SU(2) gauge theory with four fundamental flavors. From this relation, we read off how the S-duality group acts on the UV gauge coupling of the (A_3,A_3) theory.

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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

Argyres-Douglas theories and Liouville Irregular States

We study irregular states of rank-two and three in Liouville theory, based on an ansatz proposed by D. Gaiotto and J. Teschner. Using these irregular states, we evaluate asymptotic expansions of irregular conformal blocks corresponding to the partition functions of $(A_1,A_3)$ and $(A_1,D_4)$ Argyres-Douglas theories for general $Ω$-background parameters. In the limit of vanishing Liouville charge, our result reproduces strong coupling expansions of the partition functions recently obtained via the Painlevé/gauge correspondence. This suggests that the irregular conformal block for one irregular singularity of rank 3 on sphere is also related to Painlevé II. We also find that our partition functions are invariant under the action of the Weyl group of flavor symmetries once four and two-dimensional parameters are correctly identified. We finally propose a generalization of this parameter identification to general irregular states of integer rank.

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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

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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arXiv2018

Non-BPS Fractional Branes with Bose-Fermi Cancellation in Asymmetric Orbifolds

We study non-BPS D-branes in the type II string vacua with chiral space-time SUSY constructed based on the asymmetric orbifolds of $\mbox{K3} \cong T^4/{\Bbb Z}_2$ as a succeeding work of arXiv:1704.05262[hep-th]. We especially focus on the fractional D-branes that contains the contributions from the twisted sector of the ${\Bbb Z}_2$ orbifolding. We show that the cylinder partition functions for these fractional branes do not vanish, as in the cases of ordinary non-BPS D-branes. This aspect is in a sharp contrast with the bulk-type branes studied in arXiv:1704.05262[hep-th]. We then discuss the extensions of models by including the discrete torsion depending on the spin structures, and investigate whether we obtain the vanishing self-overlaps associated to the fractional branes. The existence/absence of bose-fermi cancellations both in the closed and open string spectra as well as the massless spectra in the twisted sectors crucially depend on the discrete torsion. We find that some choices of the torsion indeed realize the vanishing self-overlaps for the fractional branes, with keeping the vanishing torus partition function intact.

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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

Non-supersymmetric D-branes with Vanishing Cylinder Amplitudes in Asymmetric Orbifolds

We study the type II string vacua with chiral space-time SUSY constructed as asymmetric orbifolds of torus and $ K3 $ compactifications. Despite the fact that all the D-branes are non-BPS in any chiral SUSY vacua, we show that the relevant non-geometric vacua of asymmetric orbifolds allow rather generally configurations of D-branes which lead to vanishing cylinder amplitudes, implying the bose-fermi cancellation at each mass level of the open string spectrum. After working on simple models of toroidal asymmetric orbifolds, we focus on the asymmetric orbifolds of $ T^2 \times {\cal M} $, where $ {\cal M} $ is described by a general $ {\cal N} =4 $ SCFT with $ c=6 $ defined by the Gepner construction for $ K3 $. Even when the modular invariant partition functions in the bulk remain unchanged, the spectra of such non-BPS D-branes with the bose-fermi cancellation can vary significantly according to the choice of orbifolding.

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