120 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
A new geometry of scintillating crystals with Strip SiPMs: a PET detector with precise position and time determination
Measurement of the Time-of-Flight (TOF) of the 511 keV gammas brings an
important reduction of statistical noise in the PET image, with higher
precision time measurements producing clearer images. Scintillating crystals
are used to convert the 511 keV annihilation photon to an electron of ~511 KeV
energy via the photoelectric effect; it is necessary to determine with
precision the position and time of this conversion within the scintillating
crystal. We propose using an array of crystals cut into a specific geometry
discussed below; these crystals are read out by an array of strip SiPMs. This
technique allows individual time measurements of the first arriving
photo-electrons and to extract the best time resolution using a specific
algorithm. The final result is a precise determination of the 3D position (that
includes the depth of interaction) of the photoelectric interaction and an
improved time measurement.Comment: 15 pages, 17 figures, Published in JINS
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
Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
We study supersymmetric gauge theories with an R-symmetry, defined on
non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a
supersymmetry-preserving quotient of Euclidean AdS. We compute the exact
partition function in these theories, using the method of localization, thus
reducing the problem to the computation of one-loop determinants around a
supersymmetric locus. We evaluate the one-loop determinants employing three
different techniques: an index theorem, the method of pairing of eigenvalues,
and the heat kernel method. Along the way, we discuss aspects of supersymmetry
in manifolds with a conformal boundary, including supersymmetric actions and
boundary conditions.Comment: v3:79p, minor clarifications and references adde
The Higher Spin/Vector Model Duality
This paper is mainly a review of the dualities between Vasiliev's higher spin
gauge theories in AdS4 and three dimensional large N vector models, with focus
on the holographic calculation of correlation functions of higher spin
currents. We also present some new results in the computation of parity odd
structures in the three point functions in parity violating Vasiliev theories.Comment: 55 pages, 1 figure. Contribution to J. Phys. A special volume on
"Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev.
v2: references adde
Semichiral fields on S^2 and generalized Kahler geometry
Abstract: We study a class of two-dimensional N=(2,2) supersymmetric gauge theories, given by semichiral multiplets coupled to the usual vector multiplet. In the UV, these theories are traditional gauge theories deformed by a gauged Wess-Zumino term. In the IR, they give rise to nonlinear sigma models on noncompact generalized K\ue4hler manifolds, which contain a three-form field H and whose metric is not K\ue4hler. We place these theories on S2 and compute their partition function exactly with localization techniques. We find that the contribution of instantons to the partition function that we define is insensitive to the deformation, and discuss our results from the point of view of the generalized K\ue4hler target space. \ua9 2016, The Author(s)
The stringy instanton partition function
We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A 1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants
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