205 research outputs found
Hamiltonian perspective on generalized complex structure
In this note we clarify the relation between extended world-sheet
supersymmetry and generalized complex structure. The analysis is based on the
phase space description of a wide class of sigma models. We point out the
natural isomorphism between the group of orthogonal automorphisms of the
Courant bracket and the group of local canonical transformations of the
cotangent bundle of the loop space. Indeed this fact explains the natural
relation between the world-sheet and the geometry of T+T^*. We discuss D-branes
in this perspective.Comment: 14 pages, the version to appear in CM
Review of localization for 5d supersymmetric gauge theories
We give a pedagogical review of the localization of supersymmetric gauge
theory on 5d toric Sasaki-Einstein manifolds. We construct the cohomological
complex resulting from supersymmetry and consider its natural toric
deformations with all equivariant parameters turned on. We also give detailed
discussion on how the Sasaki-Einstein geometry permeates every aspect of the
calculation, from Killing spinor, vanishing theorems to the index theorems.Comment: This is a contribution to the review volume `Localization techniques
in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17
Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be
downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or
http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pd
5D Super Yang-Mills on Sasaki-Einstein manifolds
On any simply connected Sasaki-Einstein five dimensional manifold one can
construct a super Yang-Mills theory which preserves at least two
supersymmetries. We study the special case of toric Sasaki-Einstein manifolds
known as manifolds. We use the localisation technique to compute the
full perturbative part of the partition function. The full equivariant result
is expressed in terms of certain special function which appears to be a curious
generalisation of the triple sine function. As an application of our general
result we study the large behaviour for the case of single hypermultiplet
in adjoint representation and we derive the -behaviour in this case.Comment: 43 pages, typos and mistakes correcte
Knot Weight Systems from Graded Symplectic Geometry
We show that from an even degree symplectic NQ-manifold, whose homological
vector field Q preserves the symplectic form, one can construct a weight system
for tri-valent graphs with values in the Q-cohomology ring, satisfying the IHX
relation. Likewise, given a representation of the homological vector field, one
can construct a weight system for the chord diagrams, satisfying the IHX and
STU relations. Moreover we show that the use of the 'Gronthendieck connection'
in the construction is essential in making the weight system dependent only on
the choice of the NQ-manifold and its representation.Comment: 26 pages, revised versio
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