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Futoshi Yagi

Publications and source records attributed to Futoshi Yagi.

At least 37 records · Page 2Linked to original sources
arXiv2018

5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories

We propose 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories. From a Higgsing of the $SO(7)$ gauge theory with a hypermultiplet in the spinor representation, we construct two types of 5-brane web configurations for the pure $G_2$ gauge theory using an O5-plane or an $\widetilde{\text{O5}}$-plane. Adding flavors to the 5-brane web for the pure $G_2$ gauge theory is also discussed. Based on the obtained 5-brane webs, we compute the partition functions for the 5d $G_2$ gauge theories using the recently suggested topological vertex formulation with an O5-plane, and we find agreement with known results.

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arXiv2017

Discrete theta angle from an O5-plane

We consider 5d $\mathcal{N}=1$ $Sp(1)$ gauge theory based on a brane configuration with an O5-plane. At the UV fixed point, the theory with no matter enjoys enhanced global symmetry $SU(2)$ or $U(1)$ depending on the discrete theta angle $θ=0, π$ (mod $2π$). A naive brane configuration with an O5-plane, however, does not distinguish two different theories, as it describes the weak coupling region. We devise a technique for computing 5d Seiberg-Witten curve of the two theories from the brane web with an O5-plane. Their Seiberg-Witten curves show that their M5 configurations under the presence of OM5-planes are different. The decompactification limit of each Seiberg-Witten curve also shows distinct phase structures in their Coulomb branch leading to significantly different $(p,q)$ 5-brane configurations with an O5-plane in the strong coupling region.

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arXiv2017

5d $E_n$ Seiberg-Witten curve via toric-like diagram

We consider 5d Sp(1) gauge theory with $E_{N_f+1}$ global symmetries based on toric(-like) diagram constructed from (p,q)-web with 7-branes. We propose a systematic procedure to compute the Seiberg-Witten curve for generic toric-like diagram. For $N_f=6,7$ flavors, we explicitly compute the Seiberg-Witten curves for 5d Sp(1) gauge theory, and show that these Seiberg-Witten curves agree with already known $E_{7,8}$ results. We also discuss a generalization of the Seiberg-Witten curve to rank-N cases.

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arXiv2017

Equivalence of several descriptions for 6d SCFT

We show that the three different looking BPS partition functions, namely the elliptic genus of the 6d $\mathcal{N}=(1,0)$ $Sp(1)$ gauge theory with $10$ flavors and a tensor multiplet, the Nekrasov partition function of the 5d $\mathcal{N}=1$ $Sp(2)$ gauge theory with $10$ flavors, and the Nekrasov partition function of the 5d $\mathcal{N}=1$ $SU(3)$ gauge theory with $10$ flavors, are all equal to each other under specific maps among gauge theory parameters. This result strongly suggests that the three gauge theories have an identical UV fixed point. Type IIB 5-brane web diagrams play an essential role to compute the $SU(3)$ Nekrasov partition function as well as establishing the maps.

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arXiv2016

More on 5d descriptions of 6d SCFTs

We propose new five-dimensional gauge theory descriptions of six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories arising from type IIA brane configurations including an $ON^0$-plane. The new five-dimensional gauge theories may have $SO$, $Sp$, and $SU$ gauge groups and further broaden the landscape of ultraviolet complete five-dimensional $\mathcal{N}=1$ supersymmetric gauge theories. When we include an $O8^-$-plane in addition to an $ON^0$-plane, T-duality yields two $O7^-$-planes at the intersections of an $ON^0$-plane and two $O5^0$-planes. We propose a novel resolution of the $O7^-$-plane with four D7-branes in such a configuration, which enables us to obtain three different types of five-dimensional gauge theories, depending on whether we resolve either none or one or two $O7^-$-planes. Such different possibilities yield a new five-dimensional duality between a D-type $SU$ quiver and an $SO-Sp$ quiver theories. We also claim that a twisted circle compactification of a six-dimensional superconformal field theory may lead to a five-dimensional gauge theory different from those obtained by a simple circle compactification.

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arXiv2015

A new 5d description of 6d D-type minimal conformal matter

We propose a new 5d description of the circle-compactified 6d $(D_{N+4}, D_{N+4})$ minimal conformal matter theory which can be approached by the 6d $\mathcal{N}=(1,0)$ $Sp(N)$ gauge theory with $N_f=2N+8$ flavors and one tensor multiplet. Compactifying the brane set-up for the 6d theory, we arrive at a 5-brane Tao diagram for 5d $\mathcal{N}=1$ $SU(N+2)$ theory of the vanishing Chern-Simons level with $2N+8$ flavors. We conjecture that the 6d theory is recovered as the UV fixed point of this 5d theory. We show that the global symmetry of this 5d theory is $SO(4N+16)$ identical to that of the 6d theory by analyzing the 7-brane monodromy. By using the Tao diagram, we also find the instanton fugacity is exactly given by the circle radius. By decoupling flavors in this 5d theory, one can obtain all the 5d $SU(N+2)$ gauge theories of various Chern-Simons levels and corresponding enhanced global symmetries at the 5d UV fixed point.

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arXiv2015

Tao Probing the End of the World

We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local 1/2 K3 surface.

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arXiv2014

Fiber-Base Duality and Global Symmetry Enhancement

We show that the 5D Nekrasov partition functions enjoy the enhanced global symmetry of the UV fixed point. The fiber-base duality is responsible for the global symmetry enhancement. For $SU(2)$ with $N_f\leq 7$ flavors the fiber-base symmetry together with the manifest flavor $SO(2N_f)$ symmetry generate the $E_{N_f+1}$ global symmetry, while in the higher rank case the manifest global symmetry of the two dual theories related by the fiber-base duality map generate the symmetry enhancement. The symmetry enhancement at the level of the partition function is manifest once we chose an appropriate reparametrization for the Coulomb moduli.

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arXiv2013

Non-Lagrangian Theories from Brane Junctions

In this article we use 5-brane junctions to study the 5D T_N SCFTs corresponding to the 5D N=1 uplift of the 4D N=2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n-point functions of the q-deformed W_N Toda theories.

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arXiv2013

N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae

We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/Γin terms of blow-up formulae. We discuss the expansion of the partition function in the ε_1,ε_2 \to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety.We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories.

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arXiv2012

M5-branes, toric diagrams and gauge theory duality

In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.

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arXiv2011

Generalized matrix models and AGT correspondence at all genera

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2 gauge theory as the spectral curve of the generalized matrix model, thus providing a check of AGT correspondence at all genera.

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arXiv2011

On Effective Action of Multiple M5-branes and ABJM Action

We calculate the fluctuations from the classical multiple M5-brane solution of ABJM action which we found in the previous paper. We obtain D4-brane-like action but the gauge coupling constant depends on the spacetime coordinate. This is consistent with the expected properties of M5-brane action, although we will need to take into account the monopole operators in order to fully understand M5-branes. We also see that the Nambu-Poisson bracket is hidden in the solution.

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arXiv2010

Seiberg-Witten curve via generalized matrix model

We study the generalized matrix model which corresponds to the n-point toric Virasoro conformal block. This describes four-dimensional N=2 SU(2)^n gauge theory with circular quiver diagram by the AGT relation. We first verify that it is obtained from the perturbative calculation of the Liouville correlation function. We derive the Seiberg-Witten curve for N=2 gauge theory as a spectral curve of the generalized matrix model.

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arXiv2010

a-Maximization in N=1 Supersymmetric Spin(10) Gauge Theories

A summary is reported on our previous publications about four-dimensional N=1 supersymmetric Spin(10) gauge theory with chiral superfields in the spinor and vector representations in the non-Abelian Coulomb phase. Carrying out the method of a-maximization, we studied decoupling operators in the infrared and the renormalization flow of the theory. We also give a brief review on the non-Abelian Coulomb phase of the theory after recalling the unitarity bound and the a-maximization procedure in four-dimensional conformal field theory. This is a review article invited to International Journal of Modern Physics A.

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arXiv2009

M5-brane Solution in ABJM Theory and Three-algebra

We construct a new classical solution in the ABJM theory corresponding to M5-branes with a non-zero self-dual three form flux. This is an M-theory lift of the D4-brane solution expressed as a non-commutative plane in the three dimensional super Yang-Mills theory. We discuss that our solution is closely related with the three-algebra. We show that the corresponding configuration of the M5-brane satisfies the equations of motion in the single M5-brane action. We find the agreement between the tension of the M5-brane solution in the ABJM action and the one computed from the single M5-brane action.

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arXiv2009

New Seiberg Dualities from N=2 Dualities

We propose a number of new Seiberg dualities of N=1 quiver gauge theories. The new Seiberg dualities originate in new S-dualities of N=2 superconformal field theories recently proposed by Gaiotto. N=2 S-dual theories deformed by suitable mass terms flow to our N=1 Seiberg dual theories. We show that the number of exactly marginal operators is universal for these Seiberg dual theories and the 't Hooft anomaly matching holds for these theories. These provide strong evidence for the new Seiberg dualities. Furthermore, we study in detail the Klebanov-Witten type theory and its dual as a concrete example. We show that chiral operators and their non-linear relations match between these theories. These arguments also give non-trivial consistency checks for our proposal.

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