132 research outputs found
Index for Three Dimensional Superconformal Field Theories and Its Applications
We review aspects of superconformal indices in three dimension. Three
dimensional superconformal indices can be exactly computed by using
localization method including monopole contribution, and can be applied to
provide evidences for mirror duality, AdS_4/CFT_3 correspondence and global
symmetry enhancement of strongly coupled gauge theories. After reviewing, we
discuss the possibility of global symmetry enhancement in a finite rank of
gauge group.Comment: 14 pages, Proceedings of the Seventh International Conference Quantum
Theory and Symmetries (QTS-7) in Prague, Czech Republic, August, 2011; v2:
minor modifications, discussion of supersymmetry enhancement of abelian ABJM
theory by using an index were adde
On a modular property of N=2 superconformal theories in four dimensions
In this note we discuss several properties of the Schur index of N=2
superconformal theories in four dimensions. In particular, we study modular
properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure
Relation between the 4d superconformal index and the S^3 partition function
A relation between the 4d superconformal index and the S^3 partition function
is studied with focus on the 4d and 3d actions used in localization. In the
case of vanishing Chern-Simons levels and round S^3 we explicitly show that the
3d action is obtained from the 4d action by dimensional reduction up to terms
which do not affect the exact results. By combining this fact and a recent
proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a
formula which gives the partition function depending on the Weyl weight of
chiral multiplets, real mass parameters, FI parameters, and a squashing
parameter as a limit of the index of a parent 4d theory.Comment: 20 pages, LaTeX; v2: comments added; v3: minor corrections, version
published in JHE
Exceptional Indices
Recently a prescription to compute the superconformal index for all theories
of class S was proposed. In this paper we discuss some of the physical
information which can be extracted from this index. We derive a simple
criterion for the given theory of class S to have a decoupled free component
and for it to have enhanced flavor symmetry. Furthermore, we establish a
criterion for the "good", the "bad", and the "ugly" trichotomy of the theories.
After interpreting the prescription to compute the index with non-maximal
flavor symmetry as a residue calculus we address the computation of the index
of the bad theories. In particular we suggest explicit expressions for the
superconformal index of higher rank theories with E_n flavor symmetry, i.e. for
the Hilbert series of the multi-instanton moduli space of E_n.Comment: 33 pages, 11 figures, v2: minor correction
An E7 Surprise
We explore some curious implications of Seiberg duality for an SU(2)
four-dimensional gauge theory with eight chiral doublets. We argue that two
copies of the theory can be deformed by an exactly marginal quartic
superpotential so that they acquire an enhanced E7 flavor symmetry. We argue
that a single copy of the theory can be used to define an E7-invariant
superconformal boundary condition for a theory of 28 five-dimensional free
hypermultiplets. Finally, we derive similar statements for three-dimensional
gauge theories such as an SU(2) gauge theory with six chiral doublets or Nf=4
SQED.Comment: 27 page
Network and Seiberg Duality
We define and study a new class of 4d N=1 superconformal quiver gauge
theories associated with a planar bipartite network. While UV description is
not unique due to Seiberg duality, we can classify the IR fixed points of the
theory by a permutation, or equivalently a cell of the totally non-negative
Grassmannian. The story is similar to a bipartite network on the torus
classified by a Newton polygon. We then generalize the network to a general
bordered Riemann surface and define IR SCFT from the geometric data of a
Riemann surface. We also comment on IR R-charges and superconformal indices of
our theories.Comment: 28 pages, 28 figures; v2: minor correction
M5-branes from gauge theories on the 5-sphere
We use the 5-sphere partition functions of supersymmetric Yang-Mills theories
to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be
regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a
special limit, the perturbative partition function takes the form of the
Chern-Simons partition function on S^3. With a simple non-perturbative
completion, it becomes a 6d index which captures the degeneracy of a sector of
BPS states as well as the index version of the vacuum Casimir energy. The
Casimir energy exhibits the N^3 scaling at large N. The large N index for U(N)
gauge group also completely agrees with the supergravity index on AdS_7 x S^4.Comment: 44 pages, 1 figure, v4: ref added, clarified weak/strong coupling
behaviors of large N free energy, minor improvements, version to be published
in JHE
SQCD: A Geometric Apercu
We take new algebraic and geometric perspectives on the old subject of SQCD.
We count chiral gauge invariant operators using generating functions, or
Hilbert series, derived from the plethystic programme and the Molien-Weyl
formula. Using the character expansion technique, we also see how the global
symmetries are encoded in the generating functions. Equipped with these methods
and techniques of algorithmic algebraic geometry, we obtain the character
expansions for theories with arbitrary numbers of colours and flavours.
Moreover, computational algebraic geometry allows us to systematically study
the classical vacuum moduli space of SQCD and investigate such structures as
its irreducible components, degree and syzygies. We find the vacuum manifolds
of SQCD to be affine Calabi-Yau cones over weighted projective varieties.Comment: 49 pages, 1 figur
Exploring Curved Superspace
We systematically analyze Riemannian manifolds M that admit rigid
supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R
symmetry. We find that M admits a single supercharge, if and only if it is a
Hermitian manifold. The supercharge transforms as a scalar on M. We then
consider the restrictions imposed by the presence of additional supercharges.
Two supercharges of opposite R-charge exist on certain fibrations of a
two-torus over a Riemann surface. Upon dimensional reduction, these give rise
to an interesting class of supersymmetric geometries in three dimensions. We
further show that compact manifolds admitting two supercharges of equal
R-charge must be hyperhermitian. Finally, four supercharges imply that M is
locally isometric to M_3 x R, where M_3 is a maximally symmetric space.Comment: 39 pages; minor change
- …