We use 5-brane webs to study the two-dimensional space of supersymmetric mass deformations of higher rank generalizations of the 5d $E_1$ and $tilde{E}_1$ theories. Some of the resulting IR phases are described by IR free supersymmetric gauge theorie
s, 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 $E_1$ 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 $SU(2)times SU(2)$ if $N$ is even, and $SU(2)times U(1)$ if $N$ is odd.
We revisit the N=6 superconformal Chern-Simons-matter theories and their supergravity duals in the context of generalized symmetries. This allows us to finally clarify how the $SU(N)times SU(N)$ and $(SU(N)times SU(N))/mathbb{Z}_N$ theories, as well
as other quotient theories that have recently been discussed, fit into the holographic framework. It also resolves a long standing puzzle regarding the di-baryon operator in the $U(N)times U(N)$ theory.
We study the recently proposed AdS$_7$/CFT$_6$ dualities for a class of 6d $mathcal{N} = (1,0)$ theories that flow on the tensor branch to long linear quiver gauge theories. We find a precise agreement in the symmetries and in the spectrum of charged
states between the 6d SCFTs and their conjectured AdS$_7$ duals. We also confirm a recent conjecture that a discrete $S_N$ symmetry relating the baryons in the quiver theories is in fact gauged.
We recently conjectured a set of dualities relating two-dimensional orthogonal gauge theories with $mathcal{N}=(4,4)$ supersymmetry, analogous to Horis dualities with $mathcal{N}=(2,2)$ supersymmetry. Here we provide a quantitative test of this conje
cture by computing the elliptic genera of the dual pairs and showing that they agree. The elliptic genus of orthogonal gauge theories has multiple topological sectors that depend on the global structure of the group and on the value of a discrete $theta$ parameter. We derive the dependence on the $theta$ parameter by determining whether a given sector has $(S)Pin$ structure or not.
We refine a previous proposal for obtaining the multi-instanton partition function from the supersymmetric index of the 1d supersymmetric gauge theory on the worldline of D0-branes. We provide examples where the refinements are crucial for obtaining the correct result.
We provide further evidence that the recently constructed warped $AdS_6$ solutions in Type IIB supergravity are dual to 5d SCFTs that correspond to $(p,q)$ 5-brane webs with large numbers of like-charged external 5-branes. We study a number of specif
ic examples, including the $T_N$ theory, and identify the bulk states dual to a class of operators with ${cal O}(N)$ scaling dimensions in terms of strings and string-webs embedded in the solutions.
We construct two-dimensional N=(2,2) supersymmetric gauge theories with orthogonal and symplectic groups using branes and orientifold planes in Type IIA string theory. A number of puzzles regarding the construction, including the effect of exchanging
NS5-branes on an orientifold 2-plane, are resolved by lifting the configurations to M theory. The low energy properties and conjectured dualities of these theories are reproduced in the M-brane description. A similar construction of N=(4,4) theories with orthogonal and symplectic groups leads to new duality conjectures for these theories.
We clarify certain aspects of instanton operators in five-dimensional supersymmetric gauge theories. In particular, we show how, in the pointlike limit, they become supersymmetric and provide the natural bridge with the instantonic states contributin
g to the index as well as with the zero mode counting leading to broken current multiplets.
We propose a general formula for the perturbative large N superconformal index of 5d quiver fixed point theories that have an AdS(6)xS(4)/Z(n) supergravity dual. This index is obtained from the parent theory by projecting to orbifold-invariant states
and adding the twisted sector contributions. Our result agrees with expectations from the dual supergravity description. We test our formula against the direct computation of the index for Z(2) and Z(3) and find complete agreement.
We consider the warped AdS(6)xS^4/Z_n backgrounds dual to certain 5d quiver gauge theories. By studying dual giant gravitons in the AdS(6) geometry we are able to partially probe the Higgs branch of these theories. We show how the quantization of the
phase space of such dual giants coincides with the counting of holomorphic functions on C^2/Z_n, which is the geometric part of the Higgs branch for these theories.
