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Yutaka Yoshida

Publications and source records attributed to Yutaka Yoshida.

At least 37 records · Page 2Linked to original sources
arXiv2019

SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories

We perform SUSY localization for Coulomb branch operators of 3d $\mathcal{N}=4$ gauge theories in $\mathbb{R}^3$ with $Ω$-deformation. For the dressed monopole operators whose expectation values do not involve non-perturbative corrections, our computations reproduce the results of the so-called abelianization procedure. For the expectation values of other operators and the correlation functions of multiple operators in $U(N)$ gauge theories, we compute the non-perturbative corrections due to monopole bubbling using matrix models obtained by brane construction. We relate the results of localization to algebraic structures discussed in the mathematical literature, and also point out a similar relation for line operators in 4d $\mathcal{N}=2$ gauge theories. For $U(N)$ (quiver) gauge theories in 3d we demonstrate a direct correspondence between wall-crossing and the ordering of operators.

hep-th↗
arXiv2019

Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology

We calculate partition function and correlation functions in A-twisted 2d $\mathcal{N}=(2,2)$ theories and topologically twisted 3d $\mathcal{N}=2$ theories containing adjoint chiral multiplet with particular choices of $R$-charges and the magnetic fluxes for flavor symmetries. According to Gauge-Bethe correspondence, they correspond to Heisenberg XXX and XXZ spin chain models. We identify the partition function as the inverse of the norm of the Bethe eigenstates. Correlation functions are identified as the coefficients of the expectation value of Baxter $Q$-operators. In addition, we consider correlation functions of 2d $\mathcal{N}=(2,2)^*$ theory and their relation to equivariant quantum cohomology and equivariant integration of cotangent bundle of Grassmann manifolds. Also, we study the ring relations of supersymmetric Wilson loops in 3d $\mathcal{N}=2^*$ theory and Bethe subalgebra of XXZ spin chain model.

hep-th↗
arXiv2018

Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence

We compute the topological partition function (twisted index) of $\mathcal{N}=2$ $U(N)$ Chern-Simons theory with an adjoint chiral multiplet on $Σ_g \times S^1$. The localization technique shows that the underlying Frobenius algebra is the equivariant Verlinde algebra which is obtained from the canonical quantization of the complex Chern-Simons theory regularized by $U(1)$ equivariant parameter $t$. Our computation relies on a Bethe/Gauge correspondence which allows us to represent the equivariant Verlinde algebra in terms of the Hall-Littlewood polynomials $P_λ(x_B, t)$ with a specialization by Bethe roots $x_B$ of the $q$-boson model. We confirm a proposed duality to the Coulomb branch limit of the lens space superconformal index of four dimensional $\mathcal{N}=2$ theories for $SU(2)$ and $SU(3)$ with lower levels. In $SU(2)$ case we also present more direct computation based on Jeffrey-Kirwan residue operation.

hep-th↗
arXiv2017

Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality

We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact partition functions. Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a priori clear what should happen to the vortex dynamics. We observe that the 1d quivers for the vortices remain the same, and the net effect of the 3d duality map manifests as 1d Wall-Crossing phenomenon; Although the vortex number can shift along such duality maps, the ranks of the 1d quiver theory are unaffected, leading to a notion of fundamental vortices as basic building blocks for topological sectors. For Aharony-type duality, in particular, where one must supply extra chiral fields to couple with monopole operators on the dual side, 1d wall-crossings of an infinite number of vortex quiver theories are neatly and collectively encoded by 3d determinant of such extra chiral fields. As such, 1d wall-crossing of the vortex theory encodes the particle-vortex duality embedded in the 3d Seiberg-like duality. For $\mathcal N = 4$, the D-brane picture is used to motivate this 3d/1d connection, while, for $\mathcal N = 2$, this 3d/1d connection is used to fine-tune otherwise ambiguous vortex dynamics. We also prove some identities of 3d supersymmetric partition functions for the Aharony duality using this vortex wall-crossing interpretation.

hep-th↗
arXiv2016

Superconformal index with surface defects for class ${\cal S}_k$

We study surface defects in 4d $\mathcal{N}=1$ $SU(N)$ superconformal gauge theories of class $\mathcal{S}_k$ obtained from the 6d (1,0) theories of type $A_{N-1}$, which are worldvolume theories on $N$ M5-branes at $\mathbb{C}^2/\mathbb{Z}_k$ singularities, compactified on Riemann surfaces with punctures. First we apply a method based on Riemann surface description and obtain the superconformal index of the theories in the presence of surface defects labelled by arbitrary symmetric representations of $su(N)$. Then we propose another description for the same surface defects, which involves 4d-2d coupled systems, by identifying which 2d $\mathcal{N}=(0,2)$ theories should be coupled. We compute the index of the 4d-2d systems and reproduce the results obtained from the first method. Finally we study the 2d TQFT structure of the index for class $\mathcal{S}_{k}$ theories by obtaining several eigenfunctions and eigenvalues of the difference operators that capture the surface defects and checking their relation.

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arXiv2015

Supersymmetric index on T^2 x S^2 and elliptic genus

We study partition function of four-dimensional $\mathcal{N}=1$ supersymmetric field theory on $T^2 \times S^2$. By applying supersymmetry localization, we show that the $T^2 \times S^2$ partition function is given by elliptic genus of certain two-dimensional $\mathcal{N}=(0,2)$ theory. As an application, we discuss a relation between 4d Seiberg duality duality and 2d $(0,2)$ triality, proposed by Gadde, Gukov and Putrov. In other examples, we identify 4d theories giving elliptic genera of K3, M-strings and E-strings. In the example of K3, we find that there are two 4d theories giving the elliptic genus of K3. This would imply new four-dimensional duality.

hep-th↗
arXiv2015

Gauge/Bethe correspondence on $S^1 \times Σ_h$ and index over moduli space

We introduce two-types of topologically twisted Chern-Simons-matter theories on the direct product of circle and genus-h Riemann surface (S^1 \times Σ_h). The partition functions of first model agrees with the partition functions of a generalizations of G/G gauged WZW model. We also find that correlation functions of Wilson loops in first type Chern-Simons-matter theory coincide with correlation functions of G elements in the generalization of G/G gauged WZW model. The partition function of this model also has nice interpretations as norms of eigen states of Hamiltonian in the quantum integrable model (q-boson hopping model) and also as a geometric index over a particular moduli space. In the second-type Chern-Simons-matter theory, the partition function is related to integration over moduli space of Hitchin equation on Riemann surface.

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arXiv2014

Higgs branch localization of 3d N=2 theories

We study N=2 supersymmetric gauge theories on squashed 3-sphere and S^1xS^2. Recent studies have shown that the partition functions in a class of N=2 theories have factorized forms in terms of vortex and anti-vortex partition functions by explicitly evaluating matrix integrals obtained from Coulomb branch localization. We directly derive this structure by performing Higgs branch localization. It turns out that more general N=2 theories have this factorization property. We also discuss the factorization of supersymmetric Wilson loop.

hep-th↗
arXiv2014

Factorization of 4d N=1 superconformal index

We study the factorization of four dimensional N=1 superconformal index for U(N) (SU(N)) SQCD with N_F fundamental and anti-fundamental chiral multiplets. When both the anomaly free R-charge assignment and the traceless condition for total vorticities are satisfied, we find that the superconformal index factorizes to a pair of the elliptic uplift of the vortex partition functions. We also study the relation between open topological string and the the elliptic uplift of the vortex partition functions. In the three dimensional limit, we show index for U(N) theory reduces to the factorized form of the partition function on the three dimensional squashed sphere.

hep-th↗
arXiv2014

G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra

We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from a viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.

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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↗
arXiv2013

Localization Method for Volume of Domain-Wall Moduli Spaces

Volume of moduli space of non-Abelian BPS domain-walls is exactly obtained in U(N_c) gauge theory with N_f matters. The volume of the moduli space is formulated, without an explicit metric, by a path integral under constraints on BPS equations. The path integral over fields reduces to a finite dimensional contour integral by a localization mechanism. Our volume formula satisfies a Seiberg like duality between moduli spaces of the U(N_c) and U(N_f-N_c) non-Abelian BPS domain-walls in a strong coupling region. We also find a T-duality between domain-walls and vortices on a cylinder. The moduli space volume of non-Abelian local (N_c=N_f) vortices on the cylinder agrees exactly with that on a sphere. The volume formula reveals various geometrical properties of the moduli space.

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arXiv2013

Maximal super Yang-Mills theories on curved background with off-shell supercharges

We construct d<=7 dimensional maximally supersymmetric Yang-Mills theories on a class of curved backgrounds with off-shell supercharges. The off-shell supersymmetry is mainly a generalization of on-shell supersymmetry constructed previously by Blau. We present several examples of backgrounds and discuss the number of the preserved supersymmetries on these backgrounds. We also construct another maximally supersymmetric Yang-Mills theories on S^3 by dimensional reducing along the R-direction of N=4 super Yang-Mills theory on RxS^3.

hep-th↗
arXiv2012

Monte Carlo studies of 3d N=6 SCFT via localization method

We perform Monte Carlo study of the 3d N=6 superconformal U(N)*U(N) Chern-Simons gauge theory (ABJM theory), which is conjectured to be dual to M-theory or type IIA superstring theory on certain AdS backgrounds. Our approach is based on a localization method, which reduces the problem to the simulation of a simple matrix model. This enables us to circumvent the difficulties in the original theory such as the sign problem and the SUSY breaking on a lattice. The new approach opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes.

hep-lat↗
arXiv2012

G/G gauged WZW model and Bethe Ansatz for the phase model

We investigate the G/G gauged Wess-Zumino-Witten model on a Riemann surface from the point of view of the algebraic Bethe Ansatz for the phase model. After localization procedure is applied to the G/G gauged Wess-Zumino-Witten model, the diagonal components for group elements satisfy Bethe Ansatz equations for the phase model. We show that the partition function of the G/G gauged Wess-Zumino-Witten model is identified as the summation of norms with respect to all the eigenstates of the Hamiltonian with the fixed number of particles in the phase model. We also consider relations between the Chern-Simons theory on $S^1\timesΣ_h$ and the phase model.

hep-th↗
arXiv2012

Localization and Large N reduction on S^3 for the Planar and M-theory limit

We show a large N reduction on S^3 in a BPS sector for a broad class of theories : N>=2 supersymmetric Chern-Simons theory with any number of adjoint and bi-fundamental chiral multiplets.We show that a localization method can be applied to the reduced model and the path integral can be written by a multi-contour integral. By taking a particular localization configuration, we also show that the large N equivalence between the original theory on S^3 and the reduced model holds for the free energy and the expectation value of BPS Wilson loops. It turns out that the large N reduction on S^3 holds also for the M-theory limit.

hep-th↗
arXiv2012

Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold

We derive non-Abelian localization formulae for supersymmetric Yang-Mills-Chern-Simons theory with matters on a Seifert manifold M, which is the three-dimensional space of a circle bundle over a two-dimensional Riemann surface Σ, by using the cohomological approach introduced by Kallen. We find that the partition function and the vev of the supersymmetric Wilson loop reduces to a finite dimensional integral and summation over classical flux configurations labeled by discrete integers. We also find the partition function reduces further to just a discrete sum over integers in some cases, and evaluate the supersymmetric index (Witten index) exactly on S^1xΣ. The index completely agrees with the previous prediction from field theory and branes. We discuss a vacuum structure of the ABJM theory deduced from the localization.

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