Dyons and S-Duality in N=4 Supersymmetric Gauge Theory

We analyze the spectrum of dyons in N=4 supersymmetric Yang-Mills theory with gauge group SU(3) spontaneously broken down to U(1)xU(1). The Higgs fields select a natural basis of simple roots. Acting with S-duality on the W-boson states corresponding to simple roots leads to an orbit of BPS dyon states that are magnetically charged with respect to one of the U(1)'s. The corresponding monopole solutions can be obtained by embedding SU(2) monopoles into SU(3) and the S-duality predictions reduce to the SU(2) case. Acting with S-duality on the W-boson corresponding to a non-simple root leads to an infinite set of new S-duality predictions. The simplest of these corresponds to the existence of a harmonic form on the moduli space of SU(3) monopoles that have magnetic charge (1,1) with respect to the two U(1)'s. We argue that the moduli space is given by R^3x(R^1xM)/Z_2, where M is Euclidean Taub-NUT space, and that the latter admits the appropriate normalizable harmonic two form. We briefly discuss the generalizations to other gauge groups.Comment: 13 pages (Harvmac b), discrete identification corrected, reference adde

Vortex Strings and Four-Dimensional Gauge Dynamics

We study the low-energy quantum dynamics of vortex strings in the Higgs phase of N=2 supersymmetric QCD. The exact BPS spectrum of the stretched string is shown to coincide with the BPS spectrum of the four-dimensional parent gauge theory. Perturbative string excitations correspond to bound W-bosons and quarks while the monopoles appear as kinks on the vortex string. This provides a physical explanation for an observation by N. Dorey relating the quantum spectra of theories in two and four dimensions.Comment: 23 pages, 1 figure. v2: Two extra appendices included: one on the brane construction, the other describing the potential on the vortex moduli space. Two figures added. Typos corrected and references added. v3: BPS nature of quarks correcte

D-brane Solitons in Supersymmetric Sigma-Models

Massive D=4 N=2 supersymmetric sigma models typically admit domain wall (Q-kink) solutions and string (Q-lump) solutions, both preserving 1/2 supersymmetry. We exhibit a new static 1/4 supersymmetric `kink-lump' solution in which a string ends on a wall, and show that it has an effective realization as a BIon of the D=4 super DBI-action. It is also shown to have a time-dependent Q-kink-lump generalization which reduces to the Q-lump in a limit corresponding to infinite BI magnetic field. All these 1/4 supersymmetric sigma-model solitons are shown to be realized in M-theory as calibrated, or `Q-calibrated', M5-branes in an M-monopole background.Comment: 16 pages, 3 figures, Late

Supersymmetric black rings and three-charge supertubes

We present supergravity solutions for 1/8-supersymmetric black supertubes with three charges and three dipoles. Their reduction to five dimensions yields supersymmetric black rings with regular horizons and two independent angular momenta. The general solution contains seven independent parameters and provides the first example of non-uniqueness of supersymmetric black holes. In ten dimensions, the solutions can be realized as D1-D5-P black supertubes. We also present a worldvolume construction of a supertube that exhibits three dipoles explicitly. This description allows an arbitrary cross-section but captures only one of the angular momenta.Comment: 59 pages, 6 figures; v2: minor correction

The Moduli Space of BPS Domain Walls

N=2 SQED with several flavors admits multiple, static BPS domain wall solutions. We determine the explicit two-kink metric and examine the dynamics of colliding domain walls. The multi-kink metric has a toric Kahler structure and we reduce the Kahler potential to quadrature. In the second part of this paper, we consider semi-local vortices compactified on circle. We argue that, in the presence of a suitable Wilson line, the vortices separate into domain wall constituents. These play the role of fractional instantons in two-dimensional gauge theories and sigma-models.Comment: 16 pages, LaTex, 2 figures; factors of zeta corrected, meaning of cross-terms elucidated, further clarifying comments; (more) references adde

Overlapping Branes in M-Theory

We construct new supersymmetric solutions of $D$=11 supergravity describing $n$ orthogonally ``overlapping" membranes and fivebranes for $n$=2,\dots,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least $2^{-n}$ of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing $n$ overlapping membranes to obtain $n$ overlapping $D$-2-branes in $D$=10, $T$-duality generates new overlapping $D$-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the $D$=11 solutions. Some of the new solutions reduce to dilaton black holes in $D$=4. Additionally, we present a $D$=10 solution that describes two $D$-5-branes overlapping in a string. $T$-duality then generates further $D$=10 solutions and uplifting one of the type IIA solutions gives a new $D$=11 solution describing two fivebranes overlapping in a string.Comment: 21 pages (Harvmac b). A new discussion on solutions with four or more overlaps is presented. References adde

Electric Dipole Moment of a BPS Monopole

Monopole ``superpartner'' solutions are constructed by acting with finite, broken supersymmetry transformations on a bosonic N=2 BPS monopole. The terms beyond first order in this construction represent the backreaction of the the fermionic zero-mode state on the other fields. Because of the quantum nature of the fermionic zero-modes, the superpartner solution is necessarily operator valued. We extract the electric dipole moment operator and show that it is proportional to the fermion zero-mode angular momentum operator with a gyroelectric ratio g=2. The magnetic quadrupole operator is shown to vanish identically on all states. We comment on the usefulness of the monopole superpartner solution for a study of the long-range spin dependent dynamics of BPS monopoles.Comment: 8 pages, references and note adde

Higher spin fermions in the BTZ black hole

Recently it has been shown that the wave equations of bosonic higher spin fields in the BTZ background can be solved exactly. In this work we extend this analysis to fermionic higher spin fields. We solve the wave equations for arbitrary half-integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. These quasinormal modes are shown to agree precisely with the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We also obtain an expression for the 1-loop determinant in terms of the quasinormal modes and show it agrees with that obtained by integrating the heat kernel found by group theoretic methods.Comment: 29 page

Monopoles in the Higgs Phase

We describe new solutions of Yang-Mills-Higgs theories consisting of magnetic monopoles in a phase with fully broken gauge symmetry. Rather than spreading out radially, the magnetic field lines form flux tubes. The solution is topologically stable and, when embedded in N=2 SQCD, preserves 1/4 of the supercharges. From the perspective of the flux-tube the monopole appears as a kink. Many monopoles may be threaded onto a single flux tube and placed at arbitrary separation to create a stable, BPS necklace of solitons.Comment: 8 Pages, 1 Figure. v2: Added references and comments on 3He. v3: Another reference and corrected term in Lagrangia