Antisymmetric Matter Research Articles

(4+1)-D homogeneous anisotropic string cosmological models with dilaton and anti-symmetric matter

(4+1)-D homogeneous anisotropic string cosmological models with dilaton and anti-symmetric matter

Connecting 5d Higgs branches via Fayet-Iliopoulos deformations

We describe how the geometry of the Higgs branch of 5d superconformal field theories is transformed under movement along the extended Coulomb branch. Working directly with the (unitary) magnetic quiver, we demonstrate a correspondence between Fayet-Iliopoulos deformations in 3d and 5d mass deformations. When the Higgs branch has multiple cones, characterised by a collection of magnetic quivers, the mirror map is not globally well-defined, however we are able to utilize the correspondence to establish a local version of mirror symmetry. We give several detailed examples of deformations, including decouplings and weak-coupling limits, in (Dn, Dn) conformal matter theories, TN theory and its parent PN, for which we find new Lagrangian descriptions given by quiver gauge theories with fundamental and anti-symmetric matter.

Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers

We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in [1], by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and ℤ2 gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.

Rank-3 antisymmetric matter on 5-brane webs

We discuss Type IIB 5-brane configurations for 5d mathcal{N}=1 gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow from a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these SU(6) gauge theories.

6D attractors and black hole microstates

We find a family of AdS2×ℳ4 supersymmetric solutions of the six-dimensional F(4) gauged supergravity coupled to one vector multiplet that arises as a low energy description of massive type IIA supergravity on (warped) AdS6 × S4. ℳ4 is either a Kähler-Einstein manifold or a product of two Riemann surfaces with a constant curvature metric. These solutions correspond to the near-horizon region of a family of static magnetically charged black holes. In the case where ℳ4 is a product of Riemann surfaces, we successfully compare their entropy to a microscopic counting based on the recently computed topologically twisted index of the five-dimensional mathcal{N} = 1 USp(2N) theory with Nf fundamental flavors and an antisymmetric matter field. Furthermore, our results suggest that the near-horizon regions exhibit an attractor mechanism for the scalars in the matter coupled F(4) gauged supergravity, and we give a proposal for it.

Topologically twisted indices in five dimensions and holography

We provide a formula for the partition function of five-dimensional mathcal{N}=1 gauge theories on ℳ4 × S1, topologically twisted along ℳ4 in the presence of general background magnetic fluxes, where ℳ4 is a toric Kähler manifold. The result can be expressed as a contour integral of the product of copies of the K-theoretic Nekrasov’s partition function, summed over gauge magnetic fluxes. The formula generalizes to five dimensions the topologically twisted index of three- and four-dimensional field theories. We analyze the large N limit of the partition function and some related quantities for two theories: mathcal{N} = 2 SYM and the USp(2N) theory with Nf flavors and an antisymmetric matter field. For ℙ1×ℙ1×S1, which can be easily generalized to {varSigma}_{{mathfrak{g}}_2}times {varSigma}_{{mathfrak{g}}_1}times {S}^1 , we conjecture the form of the relevant saddle point at large N. The resulting partition function for mathcal{N} = 2 SYM scales as N3 and is in perfect agreement with the holographic results for domain walls in AdS7 × S4. The large N partition function for the USp(2N) theory scales as N5/2 and gives a prediction for the entropy of a class of magnetically charged black holes in massive type IIA supergravity.

Product group confinement in SUSY gauge theories

We propose a new set of s-confining theories with product gauge groups and no tree-level superpotential, based on a model with one antisymmetric matter field and four flavors of quarks. For each product group we find a set of gauge-invariant operators which satisfy the ’t Hooft anomaly matching conditions, and we identify the dynamically generated superpotential which reproduces the classical constraints between operators. Several of these product gauge theories confine without breaking chiral symmetry, even in cases where the classical moduli space is quantum-modified. These results may be useful for composite model building, particularly in cases where small operators of the form left(Qoverline{Q}right) are absent, or for theories with multiple natural energy scales, and may provide new ways to break supersymmetry dynamically.

5d fixed points from brane webs and O7-planes

We explore the properties of five-dimensional supersymmetric gauge theories living on 5-brane webs in orientifold 7-plane backgrounds. These include $USp(2N)$ and $SO(N)$ gauge theories with fundamental matter, as well as $SU(N)$ gauge theories with symmetric and antisymmetric matter. We find a number of new 5d fixed point theories that feature enhanced global symmetries. We also exhibit a number of new 5d dualities.

Gaiotto duality for the twisted A 2N −1 series

We study 4D $$ \mathcal{N} $$ = 2 superconformal theories that arise from the compactification of 6D $$ \mathcal{N} $$ = (2, 0) theories of type A 2N −1 on a Riemann surface C, in the presence of punctures twisted by a ℤ2 outer automorphism. We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A 3, and provide tables of properties of twisted defects up through A 9. We find atypical degenerations of Riemann surfaces that do not lead to weakly-coupled gauge groups, but to a gauge coupling pinned at a point in the interior of moduli space. As applications, we study: i) 6D representations of 4D superconformal quivers in the shape of an affine/non-affine D n Dynkin diagram, ii) S-duality of SU(4) and Sp(2) gauge theories with various combinations of fundamental and antisymmetric matter, and iii) realizations of all rank-one SCFTs predicted by Argyres and Wittig.

Dynamics of 3D SUSY gauge theories with antisymmetric matter

We investigate the IR dynamics of N=2 SUSY gauge theories in 3D with antisymmetric matter. The presence of the antisymmetric fields leads to further splitting of the Coulomb branch. Counting zero modes in the instanton background suggests that more than a single direction along the Coulomb branch may remain unlifted. We examine the case of SU(4) with one or two antisymmetric fields and various flavors in detail. Using the results for the corresponding 4D theories, we find the IR dynamics of the 3D cases via compactification and a real mass deformation. We find that for the s-confining case with two antisymmetric fields, a second unlifted Coulomb branch direction indeed appears in the low-energy dynamics. We present several non-trivial consistency checks to establish the validity of these results. We also comment on the expected structure of general s-confining theories in 3D, which might involve several unlifted Coulomb branch directions.

Chern-Simons and RG flows: contact with dualities

Contact terms in two point functions of global symmetry currents have recently been proposed as a check of Seiberg-like duality in three dimensional supersymmetric field theories. In this paper we compute the contact terms for various N=2 dual pairs in flat space. We show that the results of this computation agree with the ones obtained from localization. We study dual pairs of gauge theories with (anti-)fundamental matter fields, and some special examples of dual pairs with adjoint and antisymmetric matter fields. We also propose a duality between unitary and symplectic gauge theories.

N= 2 SU quiver with USP ends or SU ends with antisymmetric matter

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 $D(\phi)\geq3$ and superconformal field theories with only even dimensional operators $D(\phi)\geq4$.

Effective superpotential for U(N) with antisymmetric matter

We consider an = 1 U(N) gauge theory with matter in the antisymmetric representation and its conjugate, with a tree level superpotential containing at least quartic interactions for these fields. We obtain the effective glueball superpotential in the classically unbroken case, and show that it has a non-trivial N-dependence which does not factorize. We also recover additional contributions starting at order SN from the dynamics of Sp(0) factors. This can also be understood by a precise map of this theory to an Sp(2N−2) gauge theory with antisymmetric matter.

Chiral field theories from conifolds

We discuss the geometric engineering and large n transition for an N=1 U(n) chiral gauge theory with one adjoint, one conjugate symmetric, one antisymmetric and eight fundamental chiral multiplets. Our IIB realization involves an orientifold of a non-compact Calabi-Yau A_2 fibration, together with D5-branes wrapping the exceptional curves of its resolution as well as the orientifold fixed locus. We give a detailed discussion of this background and of its relation to the Hanany-Witten realization of the same theory. In particular, we argue that the T-duality relating the two constructions maps the Z_2 orientifold of the Hanany-Witten realization into a Z_4 orientifold in type IIB. We also discuss the related engineering of theories with SO/Sp gauge groups and symmetric or antisymmetric matter.

Matrix-model description of [formula omitted] gauge theories with non-hyperelliptic Seiberg–Witten curves

Using matrix-model methods we study three different N=2 models: U( N)× U( N) with matter in the bifundamental representation, U( N) with matter in the symmetric representation, and U( N) with matter in the antisymmetric representation. We find that the (singular) cubic Seiberg–Witten curves (and associated Seiberg–Witten differentials) implied by the matrix models, although of a different form from the ones previously proposed using M-theory, can be transformed into the latter and are thus physically equivalent. We also calculate the one-instanton corrections to the gauge-coupling matrix using the perturbative expansion of the matrix model. For the U( N) theories with symmetric or antisymmetric matter we use the modified matrix-model prescription for the gauge-coupling matrix discussed in our paper: Cubic curves from matrix models and generalized Konishi anomalies ( hep-th/0303268). Moreover, in the matrix model for the U( N) theory with antisymmetric matter, one is required to expand around a different vacuum than one would naively have anticipated. With these modifications of the matrix-model prescription, the results of this paper are in complete agreement with those of Seiberg–Witten theory obtained using M-theory methods.

Constructing gauge theory geometries from matrix models

We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.

On the matter of the Dijkgraaf-Vafa conjecture

With the aim of extending the gauge theory -- matrix model connection to more general matter representations, we prove that for various two-index tensors of the classical gauge groups, the perturbative contributions to the glueball superpotential reduce to matrix integrals. Contributing diagrams consist of certain combinations of spheres, disks, and projective planes, which we evaluate to four and five loop order. In the case of $Sp(N)$ with antisymmetric matter, independent results are obtained by computing the nonperturbative superpotential for $N=4,6$ and 8. Comparison with the Dijkgraaf-Vafa approach reveals agreement up to $N/2$ loops in matrix model perturbation theory, with disagreement setting in at $h=N/2+1$ loops, $h$ being the dual Coxeter number. At this order, the glueball superfield $S$ begins to obey nontrivial relations due to its underlying structure as a product of fermionic superfields. We therefore find a relatively simple example of an ${\cal N}=1$ gauge theory admitting a large $N$ expansion, whose dynamically generated superpotential differs from the one obtained in the matrix model approach.

Misleading anomaly matchings?

We investigate the low energy dynamics of N=1 supersymmetric SO(N) gauge theories with a single symmetric tensor matter field. These theories exhibit non-trivial matching of global 't Hooft anomalies at the origin of moduli space. We argue that their quantum moduli spaces possess distinct Higgs and confining branches which touch at the origin in an interacting non-Abelian Coulomb phase. The matching of anomalies between microscopic degrees of freedom and colorless moduli therefore appears to be coincidental. We discuss a formal mathematical relation between the SO(N) model and an analogous Sp(2N) theory with a single antisymmetric matter field which provides an explanation for the anomaly matching coincidence.

Symplectic SUSY gauge theories with antisymmetric matter.

We investigate the confining phase vacua of supersymmetric $\mathrm{Sp}(2{N}_{C})$ gauge theories that contain matter in both fundamental and antisymmetric representations. The moduli spaces of such models with ${N}_{F}=3$ quark flavors and ${N}_{A}=1$ antisymmetric fields are analogous to that of SUSY QCD with ${N}_{F}={N}_{C}+1$ flavors. In particular, the forms of their quantum superpotentials are fixed by classical constraints. When mass terms are coupled to ${W}_{({N}_{F}=3,{N}_{A}=1)}$ and heavy fields are integrated out, complete towers of dynamically generated superpotentials for low energy theories with fewer numbers of matter fields can be derived. Following this approach, we deduce exact superpotentials in Sp(4) and Sp(6) theories which cannot be determined by symmetry considerations or integrating in techniques. Building upon these simple symplectic group results, we also examine the ground state structures of several Sp(4)\ifmmode\times\else\texttimes\fi{}Sp(4) and Sp(6)\ifmmode\times\else\texttimes\fi{}Sp(2) models. We emphasize that the top-down approach may be used to methodically find dynamical superpotentials in many other confining supersymmetric gauge theories.

Some stability questions for higher-dimensional theories

Preliminary stability calculations are presented for a simple higher-dimensional theory containing a totally antisymmetric matter field. It is shown that the Witten instability found for the original five-dimensional Kaluza-Klein theory does not have a simple generalization. It is also shown that ground states constructed from a Freund-Rubin type ansatz (for the non-supersymmetric case) may be classically unstable against small perturbations.