115 research outputs found
On the 4d superconformal index near roots of unity: Bulk and Localized contributions
We study the expansion near roots of unity of the superconformal index of 4d
SYM. In such an expansion, middle-dimensional walls of
non-analyticity are shown to emerge in the complex analytic extension of the
integrand. These walls intersect the integration contour at infinitesimal
vicinities and come from both, the vector and chiral multiplet contributions,
and combinations thereof. We will call these intersections vector and chiral
bits, and the complementary region bulk, and show that, in the corresponding
limit, the integrals along the infinitesimal bits include, among other
contributions, factorized products of either Chern-Simons and 3d topologically
twisted partition functions.
In particular, we find that the leading asymptotic contribution to the index,
which comes from collecting all contributions coming from vector bits, reduces
to an average over a set of copies of three-dimensional
Chern-Simons partition functions in Lens spaces with , in the
presence of background flat connections. The average is
taken over the background connections, which are the positions of individual
vector bits along the contour. We also find there are other subleading
contributions, a finite number of them at finite , which include averages
over products of Chern-Simons and/or topologically -twisted
Chern-Simons-matter partition functions in three-dimensional manifolds. This
shows how in certain limits the index of 4d SYM
organizes, via an unambiguously defined coarse graining procedure, into
averages over a finite number of lower dimensional theories.Comment: 62pp. Significantly improved version, product of a deeper
understanding of some of the results presented in v1. Two new sections added,
one with a summary of results and discussion, another with further
developments. Abstract changed accordingl
Generalised asymptotic equivalence for extensive and non-extensive entropies
We extend the Hanel and Thurner asymptotic analysis to both extensive and
non-extensive entropies on the basis of a wide class of entropic forms. The
procedure is known to be capable to classify multiple entropy measures in terms
of their defining equivalence classes. Those are determined by a pair of
scaling exponents taking into account a large number of microstates as for the
thermodynamical limit. Yet, a generalisation to this formulation makes it
possible to establish an entropic connection between Markovian and
non-Markovian statistical systems through a set of fundamental entropies
, which have been studied in other contexts and exhibit, among their
attributes, two interesting aspects: They behave as additive for a large number
of degrees of freedom while they are substantially non-additive for a small
number of them. Furthermore, an ample amount of special entropy measures,
either additive or non-additive, are contained in such asymptotic
classification. Under this scheme we analyse the equivalence classes of
Tsallis, Sharma-Mittal and R\'enyi entropies and study their features in the
thermodynamic limit as well as the correspondences among them.Comment: 6 pages, 2 figure
About the phase space of SL(3) Black Holes
In this note we address some issues of recent interest, related to the
asymptotic symmetry algebra of higher spin black holes in
Chern Simons (CS) formulation. We
compute the fixed time Dirac bracket algebra that acts on two different phase
spaces. Both of these spaces contain black holes as zero modes. The result for
one of these phase spaces is explicitly shown to be isomorphic to
in first order perturbations.Comment: improved presentatio
Heterotic Mini-landscape in blow-up
Localization properties of fields in compact extra dimensions are crucial
ingredients for string model building, particularly in the framework of
orbifold compactifications. Realistic models often require a slight deviation
from the orbifold point, that can be analyzed using field theoretic methods
considering (singlet) fields with nontrivial vacuum expectation values. Some of
these fields correspond to blow-up modes that represent the resolution of
orbifold singularities. Improving on previous analyses we give here an explicit
example of the blow-up of a model from the heterotic Mini-landscape. An exact
identification of the blow-up modes at various fixed points and fixed tori with
orbifold twisted fields is given. We match the massless spectra and identify
the blow-up modes as non-universal axions of compactified string theory. We
stress the important role of the Green-Schwarz anomaly polynomial for the
description of the resolution of orbifold singularities.Comment: 34 pages, 5 figure
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