84 research outputs found
M String, Monopole String and Modular Forms
We study relations between M-strings (one-dimensional intersections of
M2-branes and M5-branes) in six dimensions and m-strings (magnetically charged
monopole strings) in five dimensions. For specific configurations, we propose
that the counting functions of BPS bound-states of M-strings capture the
elliptic genus of the moduli space of m-strings. We check this proposal for the
known cases, the Taub-NUT and Atiyah-Hitchin spaces for which we find complete
agreement. Furthermore, we analyze the modular properties of the M-string free
energies, which do not transform covariantly under SL(2,Z). However, for a
given number of M-strings, we find that there exists a unique combination of
unrefined genus-zero free energies that transforms as a Jacobi form under a
congruence subgroup of SL(2,Z). These combinations correspond to summing over
different numbers of M5-branes and make sense only if the distances between
them are all equal. We explain that this is a necessary condition for the
m-string moduli space to be factorizable into relative and center-of-mass
parts.Comment: 80 pages, 4 embedded figures, 5 long tables; v2. typos fixed; v3.
published version with title chang
Self-Duality and Self-Similarity of Little String Orbifolds
We study a class of little string theories obtained from
orbifolds of M-brane configurations. These are realised in two different ways
that are dual to each other: either as parallel M5-branes probing a
transverse singularity or M5-branes probing an
singularity. These backgrounds can further be dualised into toric, non-compact
Calabi-Yau threefolds which have double elliptic fibrations and thus
give a natural geometric description of T-duality of the little string
theories. The little string partition functions are captured by the topological
string partition function of . We analyse in detail the free energies
associated with the latter in a special region in the K\"ahler
moduli space of and discover a remarkable property: in the
Nekrasov-Shatashvili-limit, is identical to times
. This entails that the BPS degeneracies for any can
uniquely be reconstructed from the configuration, a property we
refer to as self-similarity. Moreover, as is known to display a
number of recursive structures, BPS degeneracies of little string
configurations for arbitrary as well acquire additional symmetries.
These symmetries suggest that in this special region the two little string
theories described above are self-dual under T-duality.Comment: 49 pages, 4 figure
Non-Perturbative Nekrasov Partition Function from String Theory
We calculate gauge instanton corrections to a class of higher derivative
string effective couplings introduced in [1]. We work in Type I string theory
compactified on K3xT2 and realise gauge instantons in terms of D5-branes
wrapping the internal space. In the field theory limit we reproduce the
deformed ADHM action on a general {\Omega}-background from which one can
compute the non-perturbative gauge theory partition function using
localisation. This is a non-perturbative extension of [1] and provides further
evidence for our proposal of a string theory realisation of the
{\Omega}-background.Comment: 23 page
Probing the Moduli Dependence of Refined Topological Amplitudes
With the aim of providing a worldsheet description of the refined topological
string, we continue the study of a particular class of higher derivative
couplings in the type II string effective action compactified on a
Calabi-Yau threefold. We analyse first order differential equations in the
anti-holomorphic moduli of the theory, which relate the to other
component couplings. From the point of view of the topological theory, these
equations describe the contribution of non-physical states to twisted
correlation functions and encode an obstruction for interpreting the
as the free energy of the refined topological string theory. We investigate
possibilities of lifting this obstruction by formulating conditions on the
moduli dependence under which the differential equations simplify and take the
form of generalised holomorphic anomaly equations. We further test this
approach against explicit calculations in the dual heterotic theory.Comment: 30 page
Exploring 6D origins of 5D supergravities with Chern-Simons terms
We consider five-dimensional supergravity theories with eight or sixteen
supercharges with Abelian vector fields and ungauged scalars. We address the
question under which conditions these theories can be interpreted as effective
low energy descriptions of circle reductions of anomaly free six-dimensional
theories with (1,0) or (2,0) supersymmetry. We argue that classical and
one-loop gauge- and gravitational Chern-Simons terms are instrumental for this
question.Comment: 10 pages, 1 figur
Symmetries of K3 sigma models
It is shown that the supersymmetry-preserving automorphisms of any non-linear
sigma-model on K3 generate a subgroup of the Conway group Co_1. This is the
stringy generalisation of the classical theorem, due to Mukai and Kondo,
showing that the symplectic automorphisms of any K3 manifold form a subgroup of
the Mathieu group M_{23}. The Conway group Co_1 contains the Mathieu group
M_{24} (and therefore in particular M_{23}) as a subgroup. We confirm the
predictions of the Theorem with three explicit CFT realisations of K3: the
T^4/Z_2 orbifold at the self-dual point, and the two Gepner models (2)^4 and
(1)^6. In each case we demonstrate that their symmetries do not form a subgroup
of M_{24}, but lie inside Co_1 as predicted by our Theorem.Comment: 40 page
The Effective Theory of Quantum Black Holes
We explore the quantum nature of black holes by introducing an effective
framework that takes into account deviations from the classical results. The
approach is based on introducing quantum corrections to the classical
Schwarzschild geometry in a way that is consistent with the physical scales of
the black hole and its classical symmetries. This is achieved by organizing the
quantum corrections in inverse powers of a physical distance. By solving the
system in a self-consistent way we show that the derived physical quantities,
such as event horizons, temperature and entropy can be expressed in a well
defined expansion in the inverse powers of the black hole mass. The approach
captures the general form of the quantum corrections to black hole physics
without requiring to commit to a specific model of quantum gravity.Comment: Revised version, added references, refined text and added explanatory
footnote. 23 pages, 13 figure
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