arXiv subjects

Takahiro Nishinaka

Publications and source records attributed to Takahiro Nishinaka.

At least 37 records · Page 2Linked to original sources

arXiv2017

N=2 S-duality Revisited

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), $T_{3,{3\over2}}$, emerging in this duality splits into a free piece and an interacting piece, T_X, even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about T_X by bootstrapping its chiral algebra, chi(T_X), and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for T_X and, by studying this quantity in the limit of small S^1, we make contact with a proposed S^1 reduction. Along the way, we discuss various properties of T_X: as an N=1 theory, it has flavor symmetry SU(3)XSU(2)XU(1), the central charge of chi(T_X) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of T_X theories (giving us a surprisingly close AD relative of Gaiotto's T_N theories), but it does lead to some open questions in the context of the chiral algebra / 4D N=2 SCFT correspondence.

hep-th↗

arXiv2017

On Irregular Singularity Wave Functions and Superconformal Indices

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the Schur indices of all (A_{N-1}, A_{N(n-1)-1}) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of these quantities for the (A_N, A_M) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of "Type IV" AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple "monopole vev RG" formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems.

hep-th↗

arXiv2016

Conformal Manifolds in Four Dimensions and Chiral Algebras

Any N=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral algebra is a Virasoro algebra. In this note, we consider the chiral algebras associated with interacting N=2 SCFTs possessing an exactly marginal deformation that can be interpreted as a gauge coupling (i.e., at special points on the resulting conformal manifolds, free gauge fields appear that decouple from isolated SCFT building blocks). At any point on these conformal manifolds, we argue that the associated chiral algebras possess at least three generators. In addition, we show that there are examples of SCFTs realizing such a minimal chiral algebra: they are certain points on the conformal manifold obtained by considering the low-energy limit of type IIB string theory on the three complex-dimensional hypersurface singularity x_1^3+x_2^3+x_3^3+A x_1x_2x_3+w^2=0. The associated chiral algebra is the A(6) theory of Feigin, Feigin, and Tipunin. As byproducts of our work, we argue that (i) a collection of isolated theories can be conformally gauged only if there is a SUSY moduli space associated with the corresponding symmetry current moment maps in each sector, and (ii) N=2 SCFTs with a>=c have hidden fermionic symmetries (in the sense of fermionic chiral algebra generators).

hep-th↗

arXiv2016

A Small Deformation of a Simple Theory

We study an interesting relevant deformation of the simplest interacting N=2 SCFT---the original Argyres-Douglas (AD) theory. We argue that, although this deformation is not strictly speaking Banks-Zaks like (certain operator dimensions change macroscopically), there are senses in which it constitutes a mild deformation of the parent AD theory: the exact change in the "a" anomaly is small and is essentially saturated at one loop. Moreover, contributions from IR operators that have a simple description in the UV theory reproduce a particular limit of the IR index to a remarkably high order. These results lead us to conclude that the IR theory is an interacting N=1 SCFT with particularly small "a" and "c" central charges and that this theory sheds some interesting light on the spectrum of its AD parent.

hep-th↗

arXiv2016

On 4d rank-one N=3 superconformal field theories

We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for k=1,2,3,4,6, and that the supersymmetry automatically enhances to N=4 for k=1,2. In addition, we determine the central charges a and c in terms of k, and construct the associated 2d chiral algebras, which turn out to be exotic N=2 supersymmetric W-algebras.

hep-th↗

arXiv2015

Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries

In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S^1 regime of these indices. As expected on general grounds, our study reproduces the S^3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases---with the exception of the reduction of the (A_1, D_4) SCFT---certain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as R symmetry mixing with the topological symmetries of the direct S^1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N=2 superconformal U(1)_R symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the four-dimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N=2 SCFTs.

hep-th↗

arXiv2015

Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality

We conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks of our conjectures, we demonstrate compatibility with two S-dualities, we show symmetry enhancement for special values of n, and we argue that our expressions encode a non-trivial set of renormalization group flows. Moreover, we demonstrate that, for certain values of n, our conjectures imply simple operator relations involving composites built out of the SU(2)_R currents and flavor symmetry moment maps, and we find a consistent picture in which these relations give rise to certain null states in the corresponding chiral algebras. In addition, we show that the Hall-Littlewood limits of our indices are equivalent to the corresponding Higgs branch Hilbert series. We explain this fact by considering the S^1 reductions of our theories and showing that the equivalence follows from an inequality on monopole quantum numbers whose coefficients are fixed by data of the four-dimensional parent theories. Finally, we comment on the implications of our work for more general N=2 superconformal field theories.

hep-th↗

arXiv2015

On the Superconformal Index of Argyres-Douglas Theories

We conjecture a closed-form expression for the Schur limit of the superconformal index of two infinite series of Argyres-Douglas (AD) superconformal field theories (SCFTs): the (A_1,A_{2n-3}) and the (A_1,D_{2n}) theories. While these SCFTs can be realized at special points on the Coulomb branch of certain N=2 gauge theories, their superconformal R symmetries are emergent, and hence their indices cannot be evaluated by localization. Instead, we construct the (A_1, A_{2n-3}) and (A_1, D_{2n}) indices by using a relation to two-dimensional q-deformed Yang-Mills theory and data from the class S construction. Our results generalize the indices derived from the torus partition functions of the two-dimensional chiral algebras associated with the (A_1, A_3) and (A_1, D_4) SCFTs. As checks of our conjectures, we study the consistency of our results with an S-duality recently discussed by us in collaboration with Giacomelli and Papageorgakis, we reproduce known Higgs branch relations, we check consistency with a series of renormalization group flows, and we verify that the small S^1 limits of our indices reproduce expected Cardy-like behavior. We will discuss the S^1 reduction of our indices in a separate paper.

hep-th↗

arXiv2015

Argyres-Douglas Theories and S-Duality

We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory with four fundamental flavors by Seiberg and Witten and in SU(3) gauge theory with six fundamental flavors by Argyres and Seiberg. Our constructions start by weakly gauging diagonal SU(2) and SU(3) flavor symmetry subgroups of two copies of a particular rank-one Argyres-Douglas theory (along with sufficient numbers of hypermultiplets to guarantee conformality of the gauging). As we explore the resulting conformal manifold of the SU(2) SCFT, we find an action of S-duality on the parameters of the theory that is reminiscent of Spin(8) triality. On the other hand, as we explore the conformal manifold of the SU(3) theory, we find that an exotic rank-two SCFT emerges in a dual SU(2) description.

hep-th↗

arXiv2014

Constraints on Chiral Operators in N=2 SCFTs

We study certain higher-spin chiral operators in N=2 superconformal field theories (SCFTs). In Lagrangian theories, or in theories related to Lagrangian theories by generalized Argyres-Seiberg-Gaiotto duality ("type A" theories in our classification), we give a simple superconformal representation theory proof that such operators do not exist. This argument is independent of the details of the superconformal index. We then use the index to show that if a theory is not of type A but has an N=2-preserving deformation by a relevant operator that takes it to a theory of this type in the infrared, the ultraviolet theory cannot have these higher-spin operators either. As an application of this discussion, we give a simple prescription to extract the 2a-c conformal anomaly directly from the superconformal index. We also comment on how this procedure works in the holographic limit.

hep-th↗

arXiv2014

Compact Conformal Manifolds

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such manifolds are Kahler, and so the simplest possible non-trivial compact conformal manifold in this set of geometries is a complex one-dimensional projective space. We show that such a manifold is indeed realized and give a general prescription for constructing complex N-dimensional projective space conformal manifolds as certain small N=2->N=1 breaking deformations of strongly interacting N=2 SCFTs. In many cases, our prescription reduces the construction of such spaces to a study of the N=2 chiral ring. We also give an algorithm for constructing more general compact spaces of SCFTs.

hep-th↗

arXiv2014

Topological strings and 5d T_N partition functions

We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds. The theories include certain non-Lagrangian theories such as the T_N theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T_3 theory as well as Sp(1) gauge theories with N_f = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the T_N theory. We compute the partition function of the E_7 theory via this prescription, and find the E_7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to non-toric web diagrams.

hep-th↗

arXiv2013

Wall-crossing, Toric divisor and Seiberg duality

We study the wall-crossing phenomena of BPS D4-D2-D0 states on the conifold and orbifold C^2/Z_2, from the viewpoint of the quiver quantum mechanics on the D-branes. The Kahler moduli dependence of the BPS index is translated into the FI parameter dependence of the Witten index. The wall-crossing phenomena are related to the Seiberg dualities of the quiver quantum mechanics. All the differences from the D6-D2-D0 case arise from the additional superpotential and "anti-quark" induced by the D4-brane. When the D-branes are on the conifold, the flop transition changes the duality cascade. When the D-branes are on the orbifold C^2/Z_2, the generating function of the Witten index is always given by a character of the affine SU(2) algebra. Both are consistent with the wall-crossing formula for BPS indices.

hep-th↗

arXiv2013

Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities

We construct a two-dimensional crystal melting model which reproduces the BPS index of D2-D0 states bound to a non-compact D4-brane on an arbitrary toric Calabi-Yau singularity. The crystalline structure depends on the toric divisor wrapped by the D4-brane. The molten crystals are in one-to-one correspondence with the torus fixed points of the moduli space of the quiver gauge theory on D-branes. The F- and D-term constraints of the gauge theory are regarded as a generalization of the ADHM constraints on instantons. We also show in several examples that our model is consistent with the wall-crossing formula for the BPS index.

hep-th↗

arXiv2012

Matrix models for irregular conformal blocks and Argyres-Douglas theories

As regular conformal blocks describe the N=2 superconformal gauge theories in four dimensions, irregular conformal blocks are expected to reproduce the instanton partition functions of the Argyres-Douglas theories. In this paper, we construct matrix models which reproduce the irregular conformal conformal blocks of the Liouville theory on sphere, by taking a colliding limit of the Penner-type matrix models. The resulting matrix models have not only logarithmic terms but also rational terms in the potential. We also discuss their relation to the Argyres-Douglas type theories.

hep-th↗

arXiv2012

The gravity duals of SO/USp superconformal quivers

We study the gravity duals of SO/USp superconformal quiver gauge theories realized by M5-branes wrapping on a Riemann surface ("G-curve") together with a Z_2-quotient. When the G-curve has no punctures, the gravity solutions are classified by the genus g of the G-curve and the torsion part of the four-form flux G_4. We also find that there is an interesting relation between anomaly contributions from two mysterious theories: T_{SO(2N)} theory with SO(2N)^3 flavor symmetry and \tilde{T}_{SO(2N)} theory with SO(2N) x USp(2N-2)^2 flavor symmetry. The dual gravity solutions for various SO/USp-type tails are also studied.

hep-th↗

arXiv2011

β-deformed matrix model and Nekrasov partition function

We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional \mathcal{N}=2, SU(2) supersymmetric gauge theories with N_F=2,3 and 4. By evaluating the resolvent using the loop equation for general β, we explicitly construct the first half-genus correction to the free energy and demonstrate the result coincides with the corresponding Nekrasov partition function with general Ω-background, including higher instanton contributions after modifying the relation of the Coulomb branch parameter with the filling fraction. Our approach complements the proof using the Selberg integrals directly which is useful to find the contribution in the series of instanton numbers for a given deformation parameter.

hep-th↗

arXiv2011

Evidence for Duality of Conifold from Fundamental String

We study the spectrum of BPS D5-D3-F1 states in type IIB theory, which are proposed to be dual to D4-D2-D0 states on the resolved conifold in type IIA theory. We evaluate the BPS partition functions for all values of the moduli parameter in the type IIB side, and find them completely agree with the results in the type IIA side which was obtained by using Kontsevich-Soibelman's wall-crossing formula. Our result is a quite strong evidence for string dualities on the conifold.

hep-th↗