12 research outputs found
Localization and real Jacobi forms
We calculate the elliptic genus of two dimensional abelian gauged linear
sigma models with (2,2) supersymmetry using supersymmetric localization. The
matter sector contains charged chiral multiplets as well as Stueckelberg fields
coupled to the vector multiplets. These models include theories that flow in
the infrared to non-linear sigma models with target spaces that are non-compact
Kahler manifolds with U(N) isometry and with an asymptotically linear dilaton
direction. The elliptic genera are the modular completions of mock Jacobi forms
that have been proposed recently using complementary arguments. We also compute
the elliptic genera of models that contain multiple Stueckelberg fields from
first principles.Comment: 19+1 pages, LaTeX. Minor correctio
Gauge Theory Dynamics and Calabi-Yau Moduli
We compute the exact partition function of two dimensional N=(2,2) supersymmetric gauge theories on S². For theories with SU(2|1)_A invariance, the partition function admits two equivalent representations corresponding to localization on the Coulomb branch or the Higgs branch, which includes vortex and anti-vortex excitations at the poles. For SU(2|1)_B invariant gauge theories, the partition function is localized to the Higgs branch which is generically a Kähler quotient manifold. The resulting partition functions are invariant under the renormalization group flow. For gauge theories that flow in the infrared to Calabi-Yau nonlinear sigma models, the partition functions for the SU(2|1)_A (resp SU(2|1)_B) invariant theories compute the Kähler potential on the Kähler moduli (resp. complex structure moduli) of the Calabi-Yau manifold. We also compute the elliptic genus of such theories in the presence of Stückelberg fields and show that they are modular completions of mock Jacobi forms
The Conformal Spectrum of Non-Abelian Anyons
We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents
TT\uaf -deformations in closed form
We consider the problem of exact integration of the TT\uaf -deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of det T -deformations. When the action can be shown to only depend algebraically on the background metric the solution of the deformation equation on the Lagrangian can be given in closed form in terms of solutions of the (extended) Burgers\u2019 equation. We present such examples in two and higher dimensions
Exact Results in D=2 Supersymmetric Gauge Theories
We compute exactly the partition function of two dimensional N=(2,2) gauge
theories on S^2 and show that it admits two dual descriptions: either as an
integral over the Coulomb branch or as a sum over vortex and anti-vortex
excitations on the Higgs branches of the theory. We further demonstrate that
correlation functions in two dimensional Liouville/Toda CFT compute the S^2
partition function for a class of N=(2,2) gauge theories, thereby uncovering
novel modular properties in two dimensional gauge theories. Some of these gauge
theories flow in the infrared to Calabi-Yau sigma models - such as the conifold
- and the topology changing flop transition is realized as crossing symmetry in
Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited
by demonstrating that the partition function of conjectured Seiberg dual pairs
are the same.Comment: 78 pages, LaTeX; v2: small corrections and references added; v3: JHEP
version, discussing factorization further in new appendix F; v4: sign
corrected for non simply-connected gauge grou
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The Conformal Spectrum of Non-Abelian Anyons
We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents