19 research outputs found
Rigid surface operators and S-duality: some proposals
We study surface operators in the N=4 supersymmetric Yang-Mills theories with
gauge groups SO(n) and Sp(2n). As recently shown by Gukov and Witten these
theories have a class of rigid surface operators which are expected to be
related by S-duality. The rigid surface operators are of two types, unipotent
and semisimple. We make explicit proposals for how the S-duality map should act
on unipotent surface operators. We also discuss semisimple surface operators
and make some proposals for certain subclasses of such operators.Comment: 27 pages. v2: minor changes, added referenc
Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian
We study the null fiber of a moment map related to dual pairs. We construct
an equivariant resolution of singularities of the null fiber, and get conormal
bundles of closed -orbits in the Lagrangian Grassmannian as the
categorical quotient. The conormal bundles thus obtained turn out to be a
resolution of singularities of the closure of nilpotent -orbits, which
is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference
Multi-black holes from nilpotent Lie algebra orbits
For N \ge 2 supergravities, BPS black hole solutions preserving four
supersymmetries can be superposed linearly, leading to well defined solutions
containing an arbitrary number of such BPS black holes at arbitrary positions.
Being stationary, these solutions can be understood via associated non-linear
sigma models over pseudo-Riemaniann spaces coupled to Euclidean gravity in
three spatial dimensions. As the main result of this paper, we show that
whenever this pseudo-Riemanniann space is an irreducible symmetric space G/H*,
the most general solutions of this type can be entirely characterised and
derived from the nilpotent orbits of the associated Lie algebra Lie(G). This
technique also permits the explicit computation of non-supersymmetric extremal
solutions which cannot be obtained by truncation to N=2 supergravity theories.
For maximal supergravity, we not only recover the known BPS solutions depending
on 32 independent harmonic functions, but in addition find a set of non-BPS
solutions depending on 29 harmonic functions. While the BPS solutions can be
understood within the appropriate N=2 truncation of N=8 supergravity, the
general non-BPS solutions require the whole field content of the theory.Comment: Corrected version for publication, references adde
There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models
We prove that there are no magnetically charged particle-like solutions for
Abelian models in Einstein Yang-Mills, but for non-Abelian models the
possibility remains open. An analysis of the Lie algebraic structure of the
Yang-Mills fields is essential to our results. In one key step of our analysis
we use invariant polynomials to determine which orbits of the gauge group
contain the possible asymptotic Yang-Mills field configurations. Together with
a new horizontal/vertical space decomposition of the Yang-Mills fields this
enables us to overcome some obstacles and complete a dynamical system existence
theorem for asymptotic solutions with nonzero total magnetic charge. We then
prove that these solutions cannot be extended globally for Abelian models and
begin an investigation of the details for non-Abelian models.Comment: 48 pages, 1 figur
Non-Supersymmetric Attractor Flow in Symmetric Spaces
We derive extremal black hole solutions for a variety of four dimensional
models which, after Kaluza-Klein reduction, admit a description in terms of 3D
gravity coupled to a sigma model with symmetric target space. The solutions are
in correspondence with certain nilpotent generators of the isometry group. In
particular, we provide the exact solution for a non-BPS black hole with generic
charges and asymptotic moduli in N=2 supergravity coupled to one vector
multiplet. Multi-centered solutions can also be generated with this technique.
It is shown that the non-supersymmetric solutions lack the intricate moduli
space of bound configurations that are typical of the supersymmetric case.Comment: 50 pages, 4 figures; v2: Reference added. To appear in JHE