Five-dimensional Supersymmetric Gauge Theories Research Articles

Phases of five-dimensional supersymmetric gauge theories

Five-dimensional mathcal{N} = 1 theories with gauge group U(N), SU(N), USp(2N) and SO(N) are studied at large rank through localization on a large sphere. The phase diagram of theories with fundamental hypermultiplets is universal and characterized by third order phase transitions, with the exception of U(N), that shows both second and third order transitions. The phase diagram of theories with adjoint or (anti-)symmetric hypermultiplets is also determined and found to be universal. Moreover, Wilson loops in fundamental and antisymmetric representations of any rank are analyzed in this limit. Quiver theories are discussed as well. All the results substantiate the ℱ-theorem.

Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory

We revisit the duality between five-dimensional supersymmetric gauge theories and deformations of two-dimensional Yang-Mills theory from a new perspective. We give a unified treatment of supersymmetric gauge theories in three and five dimensions using cohomological localization techniques and the Atiyah-Singer index theorem. We survey various known results in a unified framework and provide simplified derivations of localization formulas, as well as various extensions including the case of irregular Seifert fibrations. We describe the reductions to four-dimensional gauge theories, and give an extensive description of the dual two-dimensional Yang-Mills theory when the three-dimensional part of the geometry is a squashed three-sphere, including its extension to non-zero area, and a detailed analysis of the resulting matrix model. The squashing parameter b yields a further deformation of the usual q-deformation of two-dimensional Yang-Mills theory, which for rational values b2 = p/s yields a new correspondence with Chern-Simons theory on lens spaces L(p, s).

A note on instanton operators, instanton particles, and supersymmetry

We clarify certain aspects of instanton operators in five-dimensional super-symmetric gauge theories. In particular, we show how, in the pointlike limit, they become supersymmetric and provide the natural bridge with the instantonic states contributing to the index as well as with the zero mode counting leading to broken current multiplets.

Brane webs and O5-planes

We explore the properties of five-dimensional supersymmetric gauge theories living on $5$-brane webs in orientifold $5$-plane backgrounds. This allows constructing quiver gauge theories with alternating $USp(2N)$ and $SO(N)$ gauge groups with fundamental matter, and thus leads to the existence of new $5d$ fixed point theories. The web description can be further used to study non-perturbative phenomena such as enhancement of symmetry and duality. We further suggest that one can use these systems to engineer $5d$ $SO$ group with spinor matter. We present evidence for this claim.

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.

Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces

We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of non-trivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them. In some cases, the existence of these fixed points can be inferred from string duality considerations. In other cases, they arise from M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with non-trivial fixed points is a fairly complete classification of a class of singularities of Calabi-Yau threefolds which generalize the “del Pezzo contractions” and occur at higher codimension walls of the Kähler cone.