We realize four-dimensional N=2 superconformal quiver gauge theories with alternating SO and USp gauge groups as compactifications of the six-dimensional D_N theory with defects. The construction can be used to analyze infinitely strongly-coupled limits and S-dualities of such gauge theories, resulting in a new class of isolated four-dimensional N=2 superconformal field theories with SO(2N)^3 flavor symmetry.
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…
We consider the four dimensional scale invariant N=2 SU quiver gauge theories with USp(2N) ends or SU(2N) ends with antisymmetric matter representations. We argue that these theories are realized as six dimensional A_{2N-1} (0,2) theories compactified on spheres with punctures. With this realization, we can study various strongly coupled cusps in moduli space and find the S-dual theories. We find a class of isolated superconformal field theories with only odd dimensional operators $D(ϕ)\geq3$ and superconformal field theories with only even dimensional operators $D(ϕ)\geq4$.
We apply the instanton counting method to study a class of four-dimensional $\mathcal{N}=2$ supersymmetric quiver gauge theories with alternating $\mathrm{SO}$ and $\mathrm{USp}$ gauge groups. We compute the partition function in the $Ω$-background and express it as functional integrals over density functions. Applying the saddle point method, we derive the limit shape equations which determine the dominant instanton configurations in the flat space limit. The solution to the limit shape equations gives the Seiberg-Witten geometry of the low energy effective theory. As an illustrating example,…
We discuss the four dimensional models obtained by compactifying a single M5 brane probing $D_{N}$ singularity (minimal D-type $(1,0)$ conformal matter in six dimensions) on a torus with flux for abelian subgroups of the $SO(4N)$ flavor symmetry. We derive the resulting quiver field theories in four dimensions by first compactifying on a circle and relating the flux to duality domain walls in five dimensions. This leads to novel ${\cal N}=1$ dualities in 4 dimensions which arise from distinct five dimensional realizations of the circle compactifications of the D-type conformal matter.
We study partition functions of low-energy effective theories of M2-branes, whose type IIB brane constructions include orientifolds. We mainly focus on circular quiver superconformal Chern-Simons theory on $S^3$, whose gauge group is $O(2N+1)\times USp(2N)\times \cdots \times O(2N+1)\times USp(2N)$. This theory is the natural generalization of the $\mathcal{N}=5$ ABJM theory with the gauge group $O(2N+1)_{2k} \times USp(2N)_{-k}$. We find that the partition function of this type of theory has a simple relation to the one of the M2-brane theory without the orientifolds, whose gauge group is $U(…
We apply the technique of sequential deconfinement to the four dimensional $\mathcal{N}\!=\!1$ $Usp(2N)$ gauge theory with an antisymmetric field and $2F$ fundamentals. The fully deconfined frame is a length-$N$ quiver. We use this deconfined frame to prove the known self-duality of $Usp(2N)$ with an antisymmetric field and $8$ fundamentals. Along the way we encounter a subtlety: in certain quivers with degenerate holomorphic operators, a naive application of Seiberg duality rules leads to an incorrect superpotential or chiral ring. We also consider the reduction to $3d$ $\mathcal{N}\!=\!2$ th…
Inspired by the gauge/YBE correspondence this paper derives some star-triangle type relations from dualities in $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ supersymmetric quiver gauge theories. To be precise, we study two cases. The first case is the Intriligator-Pouliot duality in $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ theories. The description is performed explicitly for $N=1,2,3,4,5$ and also for $N=3k+2$, which generalizes the situation in $N=2,5$. For $N=1$ a triangle identity is obtained. For $N=2,5$ it is found that the realization of duality implies slight variations of a star-triangle relation typ…
We generalize recent construction of four-dimensional $\mathcal{N}=1$ SCFT from wrapping six-dimensional $\mathcal{N}=(2,0)$ theory on a Riemann surface to the case of $D$-type with outer-automorphism twists. This construction allows us to build various dual theories for a class of $\mathcal{N}=1$ quiver theories of $SO-USp$ type. In particular, we find there are five dual frames to $SO(2N)/USp(2N-2)/G_2$ gauge theories with $(4N-4)/4N/8$ fundamental flavors, where three of them are non-Lagrangian. We check the dualities by computing the anomaly coefficients and the superconformal indices. In …
The Argyres-Douglas (AD) theories of type $(D_n,D_m)$, realized by type IIB geometrical engineering on a single hypersurface singularity, are studied. We analyze their conformal manifolds and propose the 3d mirror theories of all theories in this class upon reduction on a circle. A subclass of the AD theories in question that admits marginal couplings is found to be $\mathrm{SO}$ or $\mathrm{USp}$ gaugings of certain $D_p(\mathrm{SO}(2N))$ and $D_p(\mathrm{USp}(2N))$ theories. For such theories, we develop a method to derive this weakly-coupled description from the Newton polygon associated to…
We discuss theoretical implications of the large k USp(2k) matrix model in zero dimension. The model appears as the matrix model of type IIB superstrings on a large $T^{6}/Z^{2}$ orientifold via the matrix twist operation. In the small volume limit, the model behaves four dimensional and its T dual is six-dimensional worldvolume theory of type I superstrings in ten spacetime dimensions. Several theoretical considerations including the analysis on planar diagrams, the commutativity of the projectors with supersymmetries and the cancellation of gauge anomalies are given, providing us with the ra…
We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to pro…
For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the identification of the precise gauge group becomes crucial when the magnetic spectrum of the theory is considered. This question is addressed in the context of Coulomb branches for $3$d $\mathcal{N}=4$ quiver gauge theories, which are moduli spaces of dressed monopole operators. Since monopole operators are characterized by their magnetic charge, the identification of the gauge group is imperative for the determination o…
AdS$_7$ solutions of massive type IIA have been classified, and are dual to a large class of six-dimensional $(1,0)$ SCFT's whose tensor branch deformations are described by linear quivers of SU groups. Quivers and AdS vacua depend solely on the group theory data of the NS5-D6-D8 brane configurations engineering the field theories. This has allowed for a direct holographic match of their $a$ conformal anomaly. In this paper we extend the match to cases where O6 and O8-planes are present, thereby introducing SO and USp groups in the quivers. In all of them we show that the $a$ anomaly computed …
A local SL(2,Z) transformation on the Type IIB brane configuration gives rise to an interesting class of superconformal field theories, known as the S-fold CFTs. Previously it has been proposed that the corresponding quiver theory has a link involving the T(U(N)) theory. In this paper, we generalise the preceding result by studying quivers that contain a T(G) link, where G is self-dual under S-duality. In particular, the cases of G = SO(2N), USp'(2N) and G_2 are examined in detail. We propose the theories that arise from an appropriate insertion of an S-fold into a brane system, in the presenc…
We consider a topological quiver matrix model which is expected to give a dual description of the instanton dynamics of topological U(N) gauge theory on D6 branes. The model is a higher dimensional analogue of the ADHM matrix model that leads to Nekrasov's partition function. The fixed points of the toric action on the moduli space are labeled by colored plane partitions. Assuming the localization theorem, we compute the partition function as an equivariant index. It turns out that the partition function does not depend on the vacuum expectation values of Higgs fields that break U(N) symmetry …
We discuss a grand unified theory (GUT) based on a $USp(32)$ GUT gauge group broken to its subgroups including a special subgroup. A GUT based on an $SO(32)$ GUT gauge group has been discussed on six-dimensional (6D) orbifold space $M^4\times T^2/\mathbb{Z}_2$. It is inspired by the $SO(32)$ string theory behind the $SU(16)$ GUT whose $SU(16)$ is broken to a special subgroup $SO(10)$. Alternative direction is to embed an $SU(16)$ gauge group into a $USp(32)$ GUT gauge group, which is inspired by a non-supersymmetric symplectic-type $USp(32)$ string theory. In a $USp(32)$ GUT, one generation of…
We explore the properties of five-dimensional supersymmetric gauge theories living on $5$-brane webs in orientifold $5$-plane backgrounds. This allows constructing quiver gauge theories with alternating $USp(2N)$ and $SO(N)$ gauge groups with fundamental matter, and thus leads to the existence of new $5d$ fixed point theories. The web description can be further used to study non-perturbative phenomena such as enhancement of symmetry and duality. We further suggest that one can use these systems to engineer $5d$ $SO$ group with spinor matter. We present evidence for this claim.
We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]^n, n=1,2. In the spirit of the AdS_7/CFT_6 correspondence massless conformal fields correspond to "supersingletons" in AdS_7. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which "massless bulk" representations are particular cases.
Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the moduli space of punctured Riemann surface M_{g,n}. We show that the weakly coupled gauge group description corresponds to a stable nodal curve, and the coupling space is actually the Deligne-Mumford compactification \bar{M}_{g,n}. We also give an algorithm to determine the weakly coupled gauge group and matter content in any duality frame.
A large family of 4d N=2 SCFT's was introduced in arXiv:1210.2886. Its elements $D_p(G)$ are labelled by a positive integer p\in N and a simply-laced Lie group G; their flavor symmetry is at least G. In the present paper we study their physics in detail. We also analyze the properties of the theories obtained by gauging the diagonal symmetry of a collection of $D_{p_i}(G)$ models. In all cases the computation of the physical quantities reduces to simple Lie-theoretical questions. To make the analysis more functorial, we replace the notion of the BPS-quiver of the N=2 QFT by the more intrinsic …
When $n$ M5 branes coincide on an A type singularity, $\mathbb{C}^2/\mathbb{Z}_k$, there is a multitude of tensionless strings which arise in the spectrum. The low energy theory when all M5 branes are separated at the singularity is given by a linear quiver with parameters $n$ and $k$. The theory has a multitude of phases, as many as partitions of $n$, each characterized by a different Higgs branch. Each such Higgs branch can be described by a Coulomb branch of a 3d $\mathcal{N}=4$ quiver. For example, at finite coupling, when all branes are separated, the quiver has a bouquet of $n$ $U(1)$ no…
We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One side of these mirror pairs are always the conventional quiver gauge theories. One of our result can also be used to determine the matter content and weakly coupled gauge groups of four dimensional N = 2 generalized quiver gauge theories derived from six dimensional A_N and D_N theory, therefore we explicitly constructed four dimensional S-duality pairs.
In this paper we detail the lattice constructions of several classes of supersymmetric quiver gauge theories in two and three Euclidean spacetime dimensions possessing exact supersymmetry at finite lattice spacing. Such constructions are obtained through the methods of topological twisting and geometric discretization of Euclidean Yang--Mills theories with eight and sixteen supercharges in two and three dimensions. We detail the lattice constructions of two-dimensional quiver gauge theories possessing four and eight supercharges and three-dimensional quiver gauge theories possessing eight supe…
We analyze the mass spectrum of spin-2 excitations around the gravity duals of "linear quiver" supersymmetric conformal field theories (SCFT's) in six dimensions. We show that for the entire family of gravity solutions it satisfies a bound which corresponds to a unitarity bound for the scaling dimension of the dual field theory operators. We determine the masses of excitations which belong to short multiplets, and for certain gravity solutions we obtain the Kaluza-Klein modes and the corresponding mass spectrum, fully and explicitly. Finally, we discuss an intuitive picture of the dual operato…
This dissertation reviews some properties of the low-energy effective actions for six dimensional open-string models. The first chapter is a pedagogical introduction about supergravity theories. In the second chapter closed strings are analyzed, with particular emphasis on type IIB, whose orientifold projection, in order to build type-I models, is the subject of the third chapter. Original results are reported in chapters 4 and 5. In chapter 4 we describe the complete coupling of (1,0) six-dimensional supergravity to tensor, vector and hypermultiplets. The generalized Green-Schwarz mechanism i…
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent she…
Cluster coordinates for a large class of Argyres-Douglas and asymptotical free theories are constructed using network on bordered Riemann surface. Such N = 2 theories are engineered using six dimensional (2, 0) theory on Riemann surface with irregular and regular singularities. The Stokes phenomenon plays an important role in our construction. Our results are expected to be very useful in studying BPS spectrum, wall crossing, and line operators of these theories, etc. In particular, we conjecture that the quiver from the network is the BPS quiver. Moreover, our construction provides a simple w…
Some admissible gauge groups of N=4 Chern-Simons gauged supergravity in three dimensions with exceptional scalar manifolds $G_{2(2)}/SO(4)$, $F_{4(4)}/USp(6)\times SU(2)$, $E_{6(2)}/SU(6)\times SU(2)$, $E_{7(-5)}/SO(12)\times SU(2)$ and $E_{8(-24)}/E_7\times SU(2)$ are identified. In particular, a complete list of all possible gauge groups is given for the theory with $G_{2(2)}/SO(4)$ coset space. We also study scalar potentials for all of these gauge groups and find some critical points. In the case of $F_{4(4)}/USp(6)\times SU(2)$ target space, we give some semisimple gauge groups which are …
Combinatorial methods are developed to find the cluster coordinates for moduli space of flat connections which is describing the Coulomb branch of higher rank N=2 theories derived by compactifying six dimensional (2,0) theory on a punctured Riemann surface. The construction starts with a triangulation of the punctured Riemann surface and a further tessellation of all the triangles. The tessellation is used to construct a bipartite network from which a quiver can be read straightforwardly. We prove that the quivers for different triangulations are related by quiver mutations and justify that th…
We propose some new infra-red dualities for $2d$ $\mathcal{N}=(0,2)$ theories. The first one relates a $USp(2N)$ gauge theory with one antisymmetric chiral, four fundamental chirals and $N$ Fermi singlets to a Landau-Ginzburg model of $N$ Fermi and $6N$ chiral fields with cubic interactions. The second one relates $SU(2)$ linear quiver gauge theories of arbitrary length $N-1$ with the addition of $N$ Fermi singlets for any non-negative integer $N$. They can be understood as a generalization of the duality between an $SU(2)$ gauge theory with four fundamental chirals and a Landau-Ginzburg model…
Compactifying N=(1,0) theories on a torus, with additional fluxes for global symmetries, we obtain N=1 supersymmetric theories in four dimensions. It is shown that for many choices of flux these models are toric quiver gauge theories with singlet fields. In particular we compare the anomalies deduced from the description of the six-dimensional theory and the anomalies of the quiver gauge theories. We also give predictions for anomalies of four-dimensional theories corresponding to general compactifications of M5-branes probing C_2/Z_k singularities.
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…
We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks associated to pairs-of-pants, and study the gauging of them as the gluing of punctures. The Riemann surface picture makes the duality invariance of the resulting quiver theories manifest: the theories associated to the same Riemann surface flow to the same nontrivial infrared fixed point. …
In this paper we explore the relation between conformal superalgebras with 64 supercharges and maximal supergravity theories in three, four and six dimensions using twistorial oscillator techniques. The massless fields of N=8 supergravity in four dimensions were shown to fit into a CPT-self-conjugate doubleton supermultiplet of the conformal superalgebra SU(2,2|8) a long time ago. We show that the fields of maximal supergravity in three dimensions can similarly be fitted into the super singleton multiplet of the conformal superalgebra OSp(16|4,R), which is related to the doubleton supermultipl…
We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver enc…
Five-dimensional $\mathcal{N}=1$ theories with gauge group $U(N)$, $SU(N)$, $USp(2N)$ and $SO(N)$ are studied at large rank through localization on a large sphere. The phase diagram of theories with fundamental hypermultiplets is universal and characterized by third order phase transitions, with the exception of $U(N)$, that shows both second and third order transitions. The phase diagram of theories with adjoint or (anti-)symmetric hypermultiplets is also determined and found to be universal. Moreover, Wilson loops in fundamental and antisymmetric representations of any rank are analyzed in t…
We consider G-equivariant dimensional reduction of Yang-Mills theory with torsion on manifolds of the form MxG/H where M is a smooth manifold, and G/H is a compact six-dimensional homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures which includes a nearly Kahler structure. We establish an equivalence between G-equivariant pseudo-holomorphic vector bundles on MxG/H and new quiver bundles on M associated to the double of a quiver Q, determined by the SU(3)-structure, with relations ensuring the absence of oriented cycles in Q. When M=R^2, …
Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative N=2 gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated to the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge…
In this paper we study compactifications of ADE type conformal matter, N M5 branes probing ADE singularity, on torus with flux for global symmetry. We systematically construct the four dimensional theories by first going to five dimensions and studying interfaces. We claim that certain interfaces can be associated with turning on flux in six dimensions. The interface models when compactified on a circle comprise building blocks for constructing four dimensional models associated to flux compactifications of six dimensional theories on a torus. The theories in four dimensions turn out to be qui…
We construct a consistent truncation of six-dimensional matter coupled $F(4)$ gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS$_2\times Σ_1$ solutions giving rise to four-dimensional orbifold solutions, AdS$_2\timesΣ_1\ltimesΣ_2$. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U$(1)^2$-gauged supergravity including all fields and arbitr…
We study N=2 supersymmetric SU(2) gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional A_1 (2,0) theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of hi…
In previous works (arXiv:1610.07916, arXiv:1711.07921, arXiv:1807.00186) we studied a class of toric Calabi-Yau threefolds which engineer six-dimensional supersymmetric gauge theories with gauge group $U(N)$ and adjoint matter. The Kähler moduli space of these manifolds can be extended through flop transformations to include regions which are described by so-called shifted toric web diagrams. In this paper we analyse gauge theories that are engineered by these shifted toric web diagrams and argue that in specific limits, some of the them engineer five-dimensional quiver gauge theories with gau…
We present a class of chiral non-supersymmetric D=4 field theories in which quadratic divergences appear only at two loops. They may be depicted as ``SUSY quivers'' in which the nodes represent a gauge group with extended e.g., N=4 SUSY whereas links represent bifundamental matter fields which transform as chiral multiplets with respect to different N=1 subgroups. One can obtain this type of field theories from simple D6-brane configurations on Type IIA string theory compactified on a six-torus. We discuss the conditions under which this kind of structure is obtained from D6-brane intersection…
We find AdS5 solutions holographically dual to compactifications of six-dimensional N=(1,0) supersymmetric field theories on Riemann surfaces with punctures. We simplify a previous analysis of supersymmetric AdS5 IIA solutions, and with a suitable Ansatz we find explicit solutions organized in three classes, where an O8--D8 stack, D6- and D4-branes are simultaneously present, localized and partially localized. The D4-branes are smeared over the Riemann surface and this is interpreted as the presence of a uniform distribution of punctures. For the first class we identify the corresponding six-d…
We explore the proposal that the six-dimensional (2,0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated N=2 superconformal theories of Argyres-Douglas type, and to two-dimensional conformal field theory with irregular states. Following the approach of Gaiotto-Teschner for the Virasoro case, we construct W_3 irregular states by colliding a single SU(3) puncture with several regular punctures of simple type. If n simple punctures are colliding with the SU(3) puncture, the resulting irregular state is a simultaneous eigenvecto…
