956 research outputs found
Supersymmetry and Homotopy
The homotopical information hidden in a supersymmetric structure is revealed
by considering deformations of a configuration manifold. This is in sharp
contrast to the usual standpoints such as Connes' programme where a geometrical
structure is rigidly fixed. For instance, we can relate supersymmetries of
types N=2n and N=(n, n) in spite of their gap due to distinction between
(even-odd)- and integer-gradings.
Our approach goes beyond the theory of real homotopy due to Quillen, Sullivan
and Tanr\'e developed, respectively, in the 60's, 70's and 80's, which exhibits
real homotopy of a 1-connected space out of its de Rham-Fock complex with
supersymmetry. Our main new step is based upon the Taylor (super-)expansion and
locality, which links differential geometry with homotopy without the
restriction of 1-connectedness. While the homotopy invariants treated so far in
relation with supersymmetry are those depending only on -grading
like the index, here we can detect new -graded homotopy invariants.
While our setup adopted here is (graded) commutative, it can be extended also
to the non-commutative cases in use of state germs (Haag-Ojima) corresponding
to a Taylor expansion
Symmetry-breaking vacua and baryon condensates in AdS/CFT
We study the gravity duals of symmetry-breaking deformations of
superconformal field theories, AdS/CFT dual to Type IIB string theory on AdS_5
x Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal
invariance and baryonic symmetries are spontaneously broken. We present a
detailed discussion of the supergravity moduli space, which involves flat form
fields on asymptotically conical Calabi-Yau manifolds, and match this to the
gauge theory vacuum moduli space. We discuss certain linearised fluctuations of
the moduli, identifying the Goldstone bosons associated with spontaneous
breaking of non-anomalous baryonic symmetries. The remaining moduli fields are
related to spontaneous breaking of anomalous baryonic symmetries. We also
elaborate on the proposal that computing condensates of baryon operators is
equivalent to computing the partition function of a non-compact Euclidean
D3-brane in the background supergravity solution, with fixed boundary
conditions at infinity.Comment: 121 pages; v2: references adde
Model Theory and Groups
The aim of the workshop was to discuss the connections between model theory and group theory. Main topics have been the interaction between geometric group theory and model theory, the study of the asymptotic behaviour of geometric properties on groups, and the model theoretic investigations of groups of finite Morley rank around the Cherlin-Zilber Conjecture
Analysis and Geometric Singularities
The Conference on “Analysis and Geometric Singularities” took place from June 27 to July 3, 2010 and had 53 participants. The organization of the meeting followed the well-established scheme, providing plenty of discussion time which was intensely used, especially by the young participants. The four survey talks were given by Gilles Carron, Jean-Michel Bismut, Ulrich Bunke and Xiaonan Ma
Twenty-five years of two-dimensional rational conformal field theory
In this article we try to give a condensed panoramic view of the development
of two-dimensional rational conformal field theory in the last twenty-five
years.Comment: A review for the 50th anniversary of the Journal of Mathematical
Physics. Some references added, typos correcte
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