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A new method to obtain the Picard-Fuchs equations of effective $N = 2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter…
We consider the 1/2 BPS circular Wilson loop in a generic N=2 SU(N) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite $N$ and in the large-N limit, using the interacting matrix model provided by…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
We propose a supersymmetric hypercolor SU(3)_H gauge theory interacting strongly at the grand unification scale, in which the hyperquark condensation breaks SU(5)_GUT down to SU(3)_C x SU(2)_L without unbroken U(1)_Y at the classical level.…
We investigate the gravitational dual of a fermionic field theory at finite temperature and charge density in two spatial dimensions, subject to a deformation by a relevant scalar operator. This makes a $(3+1)$-dimensional Einstein-Maxwell…
We construct Schubert line defects in the 3d $\mathcal{N}=2$ supersymmetric gauged linear sigma model (GLSM) with target space a partial flag manifold $X={\rm Fl}({\boldsymbol{k}};n)$, generalizing our construction for complete flag…
We study a model of four reduced staggered fields transforming in the bifundamental representation of a $SU(2)\times SU(2)$ symmetry group where just one of the SU(2) factors is gauged. This field content and symmetries are similar to a…
The $u$-plane integrals of topologically twisted $N = 2$ supersymmetric gauge theories generally contain contact terms of nonlocal topological observables. This paper proposes an interpretation of these contact terms from the point of view…
We present a model of partial compositeness arising as the IR limit of a SU(4) gauge theory with only fermionic matter. This group is one of the most promising ones among a handful of possible choices allowing a symmetry breaking pattern…
For different cohomology theories (including the Hochschild homology, Hodge cohomology, Chow groups, and Grothendieck groups of coherent sheaves), we identify the cohomology of moduli space of rank 1 perverse coherent sheaves on the blow-up…
We examine the possibility that the SU(2) gauge group of the standard model appears as the dual "magnetic" gauge group of a supersymmetric gauge theory, thus the W and Z (and through mixing, the photon) are composite (or partially…
We present a new model of composite Higgs based on a gauged SU(N) group with 4 Dirac fermions in the fundamental representation. At low energy, the model has a global symmetry SU(4)$\times$SU(4) broken to the diagonal SU(4), containing 2…
Applying advances in exact computations of supersymmetric gauge theories, we study the structure of correlation functions in two-dimensional N=(2,2) Abelian and non-Abelian gauge theories. We determine universal relations among correlation…
We investigate 2d $\mathcal{N}=(0,4)$ supersymmetric theories obtained from a topologically-twisted reduction of 4d $\mathcal{N}=2$ class $\mathcal{S}$ theories on a Riemann surface. This study addresses subtle aspects of central charges,…
We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that…
We suggest the quasiparticle picture behind the integrable structure of N=2 SYM theory,which arises if the Lax operator is considered as a Hamiltonian for the fermionic system. We compare the meaning of BPS states with the one coming from…
We study the vacuum structure of three-dimensional $SU(N)$ gauge theory coupled to a Chern-Simons term at level $k$ and to $F$ fundamental Dirac fermions. We use a large $N$ holographic description based on a D3/D7 system in type IIB string…
We investigate an Alternative Left-Right Model (ALRM) with $SU(2)_L$ as well as $SU(2)_R$ gauge groups, but unlike the traditional left-right symmetric models (LRSM) is not symmetric under the exchange of the fermion content. Interestingly,…
The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the…
Unification ideas suggest an integral treatment of fermion and boson spin and gauge-group degrees of freedom. Hence, a generalized quantum field equation, based on Dirac's, is proposed and investigated which contains gauge and flavor…