Antisymmetric Hypermultiplets Research Articles

Freezing and BPS jumping

We report a novel BPS jumping phenomenon of 5d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetric gauge theories whose brane configuration is equipped with an O7-plane. The study of the relation between O7+-plane and O7−-plane reveals that such BPS jumps take place when the Higgsing is triggered near the O7-plane upon a particular parameter tuning of the theories. We propose two types of gauge theories whose BPS spectra jump. One is the SU(2N + 8) gauge theory with a symmetric hypermultiplet converted to the SU(2N) gauge theory with an antisymmetric hypermultiplet. The other is pure SO(2N + 8) gauge theory jumping to pure Sp(N) gauge theory. We explicitly confirm our proposal through the (un)refined instanton partition functions. Furthermore, we discuss feasible generalizations involving an Op-plane for supersymmetric gauge theories of eight supercharges in four and three dimensions (p = 6, 5 respectively).

Refined topological vertex for a 5D Sp(N) gauge theories with antisymmetric matter

We consider type IIB 5-brane web diagrams for a 5D $Sp(N)$ gauge theory with an antisymmetric hypermultiplet and ${N}_{f}$ fundamental hypermultiplets. The corresponding 5-branes can be obtained by Higgsing a 5-brane web for quiver gauge theory. We use the refined topological vertex formalism to compute Nekrasov partition functions of 5D $Sp(2)$ theories with one antisymmetric hypermultiplet and flavors. Our results agree with the known results obtained from the Atiyah-Drinfeld-Hitchin-Manin method. We also discuss a particular tuning of K\"ahler parameters associated with this Higgsing.

Five-dimensional gauge theories on spheres with negative couplings

We consider supersymmetric gauge theories on S5 with a negative Yang-Mills coupling in their large N limits. Using localization we compute the partition functions and show that the pure SU(N) gauge theory descends to an SU(N/2)+N/2× SU(N/2)−N/2× SU(2) Chern-Simons gauge theory as the inverse ’t Hooft coupling is taken to negative infinity for N even. The Yang-Mills coupling of the SU(N/2)±N/2 is positive and infinite, while that on the SU(2) goes to zero. We also show that the odd N case has somewhat different behavior. We then study the SU(N/2)N/2 pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals 1 in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider USp(2N) theories with an antisymmetric hypermultiplet and Nf< 8 fundamental hypermultiplets and carry out a similar analysis. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the SU(N) theories in the large N limit.

The Cat\u2019s Cradle: deforming the higher rank E1 and {tilde{E}}_1 theories

We use 5-brane webs to study the two-dimensional space of supersymmetric mass deformations of higher rank generalizations of the 5d E1 and {tilde{E}}_1 theories. Some of the resulting IR phases are described by IR free supersymmetric gauge theories, while others correspond to interacting fixed points. The number of different phases appears to grow with the rank. The space of deformations is qualitatively different for the even and odd rank cases, but that of the even (odd) rank E1 theory is similar to that of the odd (even) rank {tilde{E}}_1 theory. One result of our analysis predicts that the supersymmetric SU(N) theory with CS level k = frac{N}{2} + 4 and a single massless antisymmetric hypermultiplet exhibits an enhanced global symmetry at the UV fixed point, given by SU(2) × SU(2) if N is even, and SU(2) × U(1) if N is odd.

Instanton operators and the Higgs branch at infinite coupling

The richness of 5d mathcal{N}=1 theories with a UV fixed point at infinite coupling is due to the existence of local disorder operators known as instanton operators. By considering the Higgs branch of SU(2) gauge theories with Nf ≤ 7 flavours at finite and infinite coupling, we write down the explicit chiral ring relations between instanton operators, the glueball superfield and mesons. Exciting phenomena appear at infinite coupling: the glueball superfield is no longer nilpotent and the classical chiral ring relations are quantum corrected by instanton operators bilinears. We also find expressions for the dressing of instanton operators of arbitrary charge. The same analysis is performed for USp(2k) with an antisymmetric hypermultiplet and pure SU(N) gauge theories.

Partition functions of 3d D ^ $$ \widehat{D} $$ -quivers and their mirror duals from 1d free fermions

We study the matrix models calculating the sphere partition functions of 3d gauge theories with $\mathcal{N}=4$ supersymmetry and a quiver structure of a $\hat D$ Dynkin diagram (where each node is a unitary gauge group). As in the case of necklace ($\hat A $) quivers, we can map the problem to that of free fermion quantum mechanics whose complicated Hamiltonian we find explicitly. Many of these theories are conjectured to be dual under mirror symmetry to certain unitary linear quivers with extra Sp nodes or antisymmetric hypermultiplets. We show that the free fermion formulations of such mirror pairs are related by a linear symplectic transformation. We then study the large N expansion of the partition function, which as in the case of the $\hat A$-quivers is given to all orders in 1/N by an Airy function. We simplify the algorithm to calculate the numerical coefficients appearing in the Airy function and evaluate them for a wide class of $\hat D$-quiver theories.

General instanton counting and 5d SCFT

Instanton partition functions of 5d $$ \mathcal{N}=1 $$ gauge theories are Witten indices for the ADHM gauged quantum mechanics with (0, 4) SUSY. We derive the integral contour prescriptions for these indices using the Jeffrey-Kirwan method, for gauge theories with hypermultiplets in various representations. The results can be used to study various 4d/5d/6d QFTs. In this paper, we study 5d SCFTs which are at the UV fixed points of 5d SYM theories. In particular, we focus on the Sp(N ) theories with N f ≤ 7 fundamental and 1 antisymmetric hypermultiplets, living on the D4-D8-O8 systems. Their superconformal indices calculated from instantons all show $$ {E_N}_{{}_f+1} $$ symmetry enhancements. We also discuss some aspects of the 6d SCFTs living on the M5-M9 system. It is crucial to understand the UV incompleteness of the 5d SYM, coming from small instantons in our problem. We explain in our examples how to fix them. As an aside, we derive the index for general gauged quantum mechanics with (0, 2) SUSY.

AdS/CFT duality and the Higgs branch of 𝒩 = 2 SYM

AbstractWe construct the AdS description of the Higgs branch of the finite 𝒩 = 2 Sp(N) gauge theory with one antisymmetric hypermultiplet and four fundamental hypermultiplets. Holography, combined with the non‐renormalization of the metric on the Higgs branch, leads to novel constraints on unknown terms in the non‐abelian Dirac‐Born‐Infeld action. These terms include non‐minimal couplings of D‐branes to bulk supergravity fields.

ANOMALOUS INTERACTIONS OF FIVE-DIMENSIONAL USp(2k) GAUGE THEORY

We consider the five-dimensional USp (2k) gauge theory which consists of one antisymmetric and nf fundamental hypermultiplets. This gauge theory is a many-probe generalization of the SU(2) gauge theory in five dimensions considered by Seiberg in the context of probing type I superstring by a D4-brane. This gauge theory can also be obtained from the USp (2k) matrix model by matrix T-dual transformations in the large k limit. We exhibit the anomalous interaction associated with this five-dimensional theory on the new phase, where the vacuum expectation values (vevs) of the scalars belonging to the antisymmetric hypermultiplet are also nonvanishing. On the Coulomb phase, the anomalous interaction has been computed in Refs. 1 and 2.

Two antisymmetric hypermultiplets in N = 2SU( N) gauge theory: Seiberg-Witten curve and M-theory interpretation

The one-instanton contribution to the prepotential for N = 2 supersymmetric gauge theories with classical groups exhibits a universality of form. We extrapolate the observed regularity to SU( N) gauge theory with two antisymmetric hypermultiplets and N f ⩽ 3 hypermultiplets in the defining representation. Using methods developed for the instanton expansion of non-hyperelliptic curves, we construct an effective quartic Seiberg-Witten curve that generates this one-instanton prepotential. We then interpret this curve in terms of an M-theoretic picture involving NS 5-branes, D4-branes, D6-branes, and orientifold sixplanes, and show that for consistency, an infinite chain of 5-branes and orientifold sixplanes is required, corresponding to a curve of infinite order.

Towards mass deformed N = 4 SO( n) and Sp( k) theories from brane configurations

We study the introduction of orientifold 6-planes in the type IIA brane configurations known as elliptic models. The N = 4 SO( n) and Sp( k) theories softly broken to N = 2 through a mass for the adjoint hypermultiplet can be realized in this framework in the presence of two orientifold planes with opposite RR charge. A large class of β = 0 models is solved for vanishing sum of hypermultiplet masses by embedding the type IIA configuration into M-theory. We also find a geometric interpretation of Montonen-Olive duality based on the properties of the curves. We make a proposal for the introduction of non-vanishing sum of hypermultiplet masses in a sub-class of models. In the presence of two negatively charged orientifold planes and four D6-branes other interesting β = 0 theories are constructed, e.g. Sp( k) with four flavours and a massive antisymmetric hypermultiplet. We comment on the difficulties in obtaining the curves within our framework due to the arbitrary positions of the D6-branes.