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A bstract The mass spectrum of 1 + 1dimensional SU( N ) gauge theory coupled to a Majorana fermion in the adjoint representation has been studied in the large N limit using LightCone Quantization. Here we extend this approach to theories with small values of N , exhibiting explicit results for N = 2 , 3, and 4. In the context of Discretized LightCone Quantization, we develop a procedure based on the CayleyHamilton theorem for determining which states of the large N theory become null at finite N . For the lowlying bound states, we find that the squared masses divided by g 2 N , where g is the gauge coupling, have very weak dependence on N . The coefficients of the 1 /N 2 corrections to their large N values are surprisingly small. When the adjoint fermion is massless, we observe exact degeneracies that we explain in terms of a KacMoody algebra construction and charge conjugation symmetry. When the squared mass of the adjoint fermion is tuned to g 2 N/π , we find evidence that the spectrum exhibits bosonfermion degeneracies, in agreement with the supersymmetry of the model at any value of N .more » « lessFree, publiclyaccessible full text available April 1, 2024

A bstract Threedimensional $$ \mathcal{N} $$ N = 4 superconformal field theories contain 1d topological sectors consisting of twisted linear combinations of halfBPS local operators that can be inserted anywhere along a line. After a conformal mapping to a round threesphere, the 1d sectors are now defined on a great circle of S 3 . We show that the 1d topological sectors are preserved under the squashing of the sphere. For gauge theories with matter hypermultiplets, we use supersymmetric localization to derive an explicit description of the topological sector associated with the Higgs branch. Furthermore, we find that the dependence of the 1d correlation functions on the squashing parameter b can be removed after appropriate rescalings. One can introduce real mass and FayetIliopolous parameters that, after appropriate rescalings, modify the 1d theory on the squashed sphere precisely as they do on the round sphere. In addition, we also show that when a generic 3d $$ \mathcal{N} $$ N = 4 theory is deformed by real mass parameters, this deformation translates into a universal deformation of the corresponding 1d theory.more » « less

A bstract We study the massdeformed sphere free energy of threedimensional $$ \mathcal{N} $$ N = 2 superconformal field theories with holographic duals. Building on previous observations, we conjecture a proportionality relation between the sphere free energy on the boundary and the prepotential of the fourdimensional $$ \mathcal{N} $$ N = 2 supergravity theory in the bulk. We verify this formula by explicit computation in several examples of supergravity theories with vector multiplets and hypermultiplets.more » « less