A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory

Super twistor space admits a certain (super) complex structure deformation that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in twistor string theory this deformation corresponds to augmenting N=4 super Yang-Mills theory by a mass term for the left-chirality spinors. In this paper we analyze this proposal in more detail. We calculate 4-particle scattering amplitudes of fermions, gluons and scalars and show that they are supported on holomorphic curves in the deformed twistor space.Comment: 52 pages, 15 figure

Fuzzy Scalar Field Theory as a Multitrace Matrix Model

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement

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.Comment: 1+19 pages, presentation improved, minor corrections, published versio

Fuzzy Scalar Field Theory as Matrix Quantum Mechanics

We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed external matrices. These terms can be approximated by multitrace expressions using a group theoretical method developed recently. The resulting matrix model is accessible to the standard techniques of matrix quantum mechanics.Comment: 1+17 pages, 4 figures, minor improvements, version published in JHE

Twistor Strings with Flavour

We explore the tree-level description of a class of N=2 UV-finite SYM theories with fundamental flavour within a topological B-model twistor string framework. In particular, we identify the twistor dual of the Sp(N) gauge theory with one antisymmetric and four fundamental hypermultiplets, as well as that of the SU(N) theory with 2N hypermultiplets. This is achieved by suitably orientifolding/orbifolding the original N=4 setup of Witten and adding a certain number of new topological 'flavour'-branes at the orientifold/orbifold fixed planes to provide the fundamental matter. We further comment on the appearance of these objects in the B-model on CP(3|4). An interesting aspect of our construction is that, unlike the IIB description of these theories in terms of D3 and D7-branes, on the twistor side part of the global flavour symmetry is realised geometrically. We provide evidence for this correspondence by calculating and matching amplitudes on both sides.Comment: 38+12 pages; uses axodraw.sty. v2: References added, minor clarification

Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere

We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of different regimes of the model in a precise and reliable way. We study the modes associated to different momenta and the role they play in the ``striped phase'', pointing out a consistent interpretation which is corroborated by our data, and which sheds further light on the results obtained in some previous works. Next, we test a quantitative, non-trivial theoretical prediction for this model, which has been formulated in the literature: The existence of an eigenvalue sector characterised by a precise probability density, and the emergence of the phase transition associated with the opening of a gap around the origin in the eigenvalue distribution. The theoretical predictions are confirmed by our numerical results. Finally, we propose a possible method to detect numerically the non-commutative anomaly predicted in a one-loop perturbative analysis of the model, which is expected to induce a distortion of the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study of the eigenvalue distribution, added figures, tables and references, typos corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references added, technical details about the tests at small matrix size skipped, version published in JHE

Matrix Models and D-branes in Twistor String Theory

We construct two matrix models from twistor string theory: one by dimensional reduction onto a rational curve and another one by introducing noncommutative coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment on the interpretation of our matrix models in terms of topological D-branes and relate them to a recently proposed string field theory. By extending one of the models, we can carry over all the ingredients of the super ADHM construction to a D-brane configuration in the supertwistor space P^(3|4). Eventually, we present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio

A projective Dirac operator on CP^2 within fuzzy geometry

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos correcte

The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio