Non-supersymmetric gauge theories from D-branes in type 0 string theory

We construct non-supersymmetric four-dimensional gauge theories arising as effective theories of D-branes placed on various singularities in Type 0B string theory. We mostly focus on models which are conformal in the large-N limit and present both examples appearing on self-dual D3-branes on orbifold singularities and examples including orientifold planes. Moreover, we derive type 0 Hanany-Witten setups with NS 5-branes intersected by D-branes and the corresponding rules for determining the massless spectra. Finally, we discuss possible duality symmetries (Seiberg duality) for non-supersymmetric gauge theories within this framework.     

Constructing Self-Dual Strings

We present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation. Our construction finds a natural interpretation in terms of gerbes, which we develop in some detail. We also comment on a possible extension to stacks of multiple M5-branes.     

Evidence for heterotic - Type I string duality

A study is made of the implications of heterotic string T-duality and extended gauge symmetry for the conjectured equivalence of heterotic and Type I superstrings. While at first sight heterotic string world-sheet dynamics appears to conflict with Type I perturbation theory, a closer look shows that Type I perturbation theory “miraculously” breaks down, in some cases via novel mechanisms, whenever the heterotic string has massless particles not present in Type I perturbation theory. This strongly suggests that the two theories actually are equivalent. As further evidence in the same direction, we show that the Dirichlet one-brane of Type I string theory has the same world-sheet structure as the heterotic string.     

Born–Infeld–Chern–Simons theory: Hamiltonian embedding,duality and bosonization

In this paper we study in detail the equivalence of the recently introduced Born–Infeld self-dual model to the Abelian Born–Infeld–Chern–Simons model in 2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme, to embed the Born–Infeld self-dual model to a gauge system and show that the embedded model is equivalent to Abelian Born–Infeld–Chern–Simons theory. Next, using Buscher's duality procedure, we demonstrate this equivalence in a covariant Lagrangian formulation and also derive the mapping between the n-point correlators of the (dual) field strength in Born–Infeld–Chern–Simons theory and of basic field in Born–Infeld self-dual model. Using this equivalence, the bosonization of a massive Dirac theory with a non-polynomial Thirring type current–current coupling, to leading order in (inverse) fermion mass is also discussed. We also rederive it using a master Lagrangian. Finally, the operator equivalence between the fermionic current and (dual) field strength of Born–Infeld–Chern–Simons theory is deduced at the level of correlators and using this the current–current commutators are obtained.     

BLG and M5

We discuss the interpretation of the three-dimensional N = 8 superconformal Chern-Simons-matter theory with the gauge group of volume preserving diffeomorphisms as a model describing a six-dimensional self-dual gauge field coupled to scalars and spinors and its possible relation to the M5-brane     

一种自对偶理论的规范不变形式及其量子化

对于一种新提出的自对偶场与规范场耦合的拉氏理论,本文给出相应的单上闭链,即Wess-Zumino项,构造了这种理论的规范不变的形式。利用正则量子化方法并通过选取适当的规范固定条件,证明了这规范不变的形式等价于原来的规范非不变的形式。此外,利用Batalin-Fradkin-Vilkovisky量子化方法,进一步指出这种等价性与规范固定条件的选择是无关的。 关键词：     

Gauge theories of Josephson junction arrays

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetric Kalb-Ramond gauge field.     

On non-supersymmetric CFT in four dimensions

We show that the theories on the self-dual D3-branes of Type 0 string theory are in the class of the previously considered tadpole-free orbifolds of theory (although they have SO(6) global symmetry) and hence have vanishing beta function in the planar limit to all orders in 't Hooft coupling. Also, all planar amplitudes in this theory are equal to those of theory, up to a rescaling of the coupling.     

Semi-simple unification on T/Z12 orientifold in the type IIB supergravity

The semi-simple unification model based on SU(5)_GUT×U(3)_H gauge group is an interesting extension of the minimal SU(5)_GUT grand unification theory (GUT), since it solves the two serious problems in the standard GUT: the triplet–doublet splitting problem and the presence of dangerous dimension five operators for proton decay. Here, the extra U(3)_H gauge interaction plays a crucial role on the GUT breaking. In this Letter, we show that the full multiplet structure of the U(3)_H sector required for the desired GUT breaking is reproduced naturally on T⁶/Z₁₂ orientifold in the type IIB supergravity with a D3–D7 system. The SU(5)_GUT vector multiplet lives on D7-branes and the U(3)_H sector resides on D3-branes. We also show that various interesting features in the original SU(5)_GUT×U(3)_H model are explained in the present brane-world scenario. A possible extension to the type IIB string theory is also discussed.     

Heterotic p-branes from massive sigma models

We explicitly construct massive (0,4) supersymmetric ADHM sigma models which have heterotic p-brane solitons as their conformal fixed points. These yield the familiar gauge 5-brane and a new 1-brane solution which preserve half and a quarter of the space-time supersymmetry, respectively. We also discuss an analogous construction for the type 11 NS-NS p-branes using (4,4) supersymmetric models.     

The twistor theory of equations of KdV type: I

This article is the first of two concerned with the development of the theory of equations of KdV type from the point of view of twistor theory and the self-dual Yang-Mills equations. A hierarchy on the self-dual Yang-Mills equations is introduced and it is shown that a certain reduction of this hierarchy is equivalent to then-generalized KdV-hierarchy. It also emerges that each flow of then-KdV hierarchy is a reduction of the self-dual Yang-Mills equations with gauge group SL _n . It is further shown that solutions of the self-dual Yang-Mills hierarchy and their reductions arise via a generalized Ward transform from holomorphic vector bundles over a twistor space. Explicit examples of such bundles are given and the Ward transform is implemented to yield a large class of explicit solutions of then-KdV equations. It is also shown that the construction of Segal and Wilson of solutions of then-KdV equations from loop groups is contained in our approach as an ansatz for the construction of a class of holomorphic bundles on twistor space.A summary of the results of the second part of this work appears in the Introduction.Most of this work was done while Darby Fellow of Mathematics at Lincoln College, Oxford     

Some BPS configurations of the BLG theory

We obtain BPS configurations of the BLG theory and its variant including mass terms for scalars and fermions in addition to a background field with different world-volume and R-symmetries. Three cases are considered, with world-volume symmetries SO(1,1) and SO(2) and preserving different amounts of supersymmetry. In the former case we obtain a singular configuration preserving N=(3,3) supersymmetry and an one-quarter BPS configuration corresponding to intersecting M2-M5-M5-branes. In the latter instance the BPS equations are reduced to those in the self-dual Chern-Simons theory with two complex scalars. In want of an exact solution, we find a topological vortex solution numerically in this case. Other solutions are given by combinations of domain walls.     

Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

We study some aspects of Maldacena's large-N correspondence between superconformal gauge theory on the D3-brane and maximal supergravity on AdS by introducing macroscopic strings as heavy (anti-) quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on a D3-brane world-volume. We first study deformation and fluctuation of D3-branes when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for the macroscopic string in anti-de Sitter supergravity. As a by-product we clarify how Polchinski's Dirichlet and Neumann open string boundary conditions arise dynamically. We then study the non-BPS macroscopic string–anti-string pair configuration as a physical realization of a heavy quark Wilson loop. We obtain the static potential from the supergravity side and find that the potential exhibits non-analyticity of the square-root branch cut in the 't Hooft coupling parameter. We put forward non-analyticity as a prediction for large-N gauge theory in the strong 't Hooft coupling limit. By turning on the Ramond–Ramond zero-form potential, we also study the vacuum angle dependence of the static potential. We finally discuss the possible dynamical realization of the heavy N-prong string junction and of the large-N loop equation via a local electric field and string recoil thereof. Throughout comparisons of the AdS–CFT correspondence, we find that a crucial role is played by “geometric duality” between the UV and IR scales in directions perpendicular to the D3-brane and parallel ones, explaining how the AdS spacetime geometry emerges out of four-dimensional gauge theory at strong coupling. Received: 21 September 2001 / Published online: 12 November 2001     

Self-dual Vortices in Schrödinger-Chern-Simons Model

By making use of the U(1) gauge potential decomposition theory and the φ-mapping topological current theory, we investigate the Schrödinger-Chern-Simons model in the thin-film superconductor system and obtain an exact Bogomolny self-dual equation with a topological term. It is revealed that there exist self-dual vortices in the system. We study the inner topological structure of the self-dual vortices and show that their topological charges are topologically quantized and labeled by Hopf indices and Brouwer degrees. Furthermore, the vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the vector field φ.     

Duality in non-linear BF models: equivalence between self-dual and topologically massive Born–Infeld BF models

We study the dual equivalence between the non-linear generalization of the self-dual (NSD_BF) and the topologically massive BF models with particular emphasis on the non-linear electrodynamics proposed by Born and Infeld. This is done through a dynamical gauge embedding of the non-linear self-dual model yielding to a gauge invariant and dynamically equivalent theory. We clearly show that non-polinomial NSD_BF models can be map, through a properly defined duality transformation into TM_BF actions. The general result obtained is then particularized for a number of examples, including the Born–Infeld-BF (BIBF) model that has experienced a revival in the recent literature.     

Noncommutative M-branes from covariant open supermembranes

We discuss an open supermembrane in the presence of a constant three-form. The boundary conditions to ensure the κ-invariance of the action lead to possible Dirichlet branes. It is shown that a noncommutative (NC) M5-brane is possible as a boundary and the self-duality condition that the flux on the world-volume satisfies is derived from the requirement of the κ-symmetry. We also find that the open supermembrane can attach to each of infinitely many M2-branes on an M5-brane, namely a strong flux limit of the NC M5-brane.     

Pohlmeyer reduction of superstring sigma model

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS₅×S⁵ superstring world-sheet theory in terms of physical degrees of freedom we construct the “Pohlmeyer-reduced” version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting equations can be obtained from a Lagrangian of a non-Abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. The small-fluctuation spectrum near the trivial vacuum contains 8 bosonic and 8 fermionic degrees of freedom with equal mass. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS₂×S² superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.