124538641
TASI Lectures on Solitons Instantons, Monopoles, Vortices and Kinks
These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory. The lectures consist of four sections, each dealing with a different soliton. We start with instantons and work down in co-dimension to monopoles, vortices and, eventually, domain walls. Emphasis is placed on the moduli space of solitons and, in particular, on the web of connections that links solitons of different types. The D-brane realization of the ADHM and Nahm construction for instantons and monopoles is reviewed, together with related constructions for vortices and domain walls. Each lecture ends with a series of vignettes detailing the roles solitons play in the quantum dynamics of supersymmetric gauge theories in various dimensions. This includes applications to the AdS/CFT correspondence, little string theory, S-duality, cosmic strings, and the quantitative correspondence between 2d sigma models and 4d gauge theories.
5375662
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.
10464021
Monopoles, vortices, domain walls and D-branes: The Rules of interaction
Non-abelian gauge theories in the Higgs phase admit a startling variety of BPS solitons. These include domain walls, vortex strings, confined monopoles threaded on vortex strings, vortex strings ending on domain walls, monopoles threaded on strings ending on domain walls, and more. After presenting a self-contained review of these objects, including several new results on the dynamics of domain walls, we go on to examine the possible interactions of solitons of various types. We point out the existence of a classical binding energy when the string ends on the domain wall which can be thought of as a BPS boojum with negative mass. We present an index theorem for domain walls in non-abelian gauge theories. We also answer questions such as: Which strings can end on which walls? What happens when monopoles pass through domain walls? What happens when domain walls pass through each other?
2897012
Dyonic instantons in five-dimensional gauge theories
Abstract We show that there exist finite energy, non-singular instanton solutions for five-dimensional theories with broken gauge symmetry. The soliton is supported against collapse by a non-zero electric charge. The low-energy dynamics of these solutions is described by motion on the ADHM moduli space with potential.
9118453
The dS/dS Correspondence
We present a holographic duality for the de Sitter static patch which consolidates basic features of its geometry and the behavior of gravity and brane probes, valid on timescales short compared to the decay or Poincare recurrence times. Namely de Sitter spacetime dSd(R) in d dimensions with curvature radius R is holographically dual to two conformal field theories on dSd−1(R), cut off at an energy scale 1/R where they couple to each other and to d − 1 dimensional gravity. As part of our analysis, we study brane probes in de Sitter and thermal Anti de Sitter spaces, and interpret the terms in the corresponding DBI action via strongly coupled thermal field theory. This provides a dual field theoretic interpretation of the fact that probes take forever to reach a horizon in general relativity.
119234030
The partonic nature of instantons
In both Yang-Mills theories and sigma models, instantons are endowed with degrees of freedom associated to their scale size and orientation. It has long been conjectured that these degrees of freedom have a dual interpretation as the positions of partonic constituents of the instanton. These conjectures are usually framed in d = 3+1 and d = 1+1 dimensions respectively where the partons are supposed to be responsible for confinement and other strong coupling phenomena. We revisit this partonic interpretation of instantons in the context of d = 4+1 and d = 2+1 dimensions. Here the instantons are particle-like solitons and the theories are non-renormalizable. We present an explicit and calculable model in d = 2+1 dimensions where the single soliton in the CPN sigma-model can be shown to be a multi-particle state whose partons are identified with the ultra-violet degrees of freedom which render the theory well-defined at high energies. We introduce a number of methods which reveal the partons inside the soliton, including deforming the sigma model and a dual version of the Bogomolnyi equations. We conjecture that partons inside Yang-Mills instantons hold the key to understanding the ultra-violet completion of five-dimensional gauge theories.
3058516
Quantitative conditions do not guarantee the validity of the adiabatic approximation.
In this Letter, we point out that the widely used quantitative conditions in the adiabatic theorem are insufficient in that they do not guarantee the validity of the adiabatic approximation. We also reexamine the inconsistency issue raised by Marzlin and Sanders [Phys. Rev. Lett. 93, 160408 (2004)] and elucidate the underlying cause.