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Manifestly N=2 supersymmetric regularization for N=2 supersymmetric field theories
We formulate the higher covariant derivative regularization for N=2
supersymmetric gauge theories in N=2 harmonic superspace. This regularization
is constructed by adding the N=2 supersymmetric higher derivative term to the
classical action and inserting the N=2 supersymmetric Pauli--Villars
determinants into the generating functional for removing one-loop divergencies.
Unlike all other regularization schemes in N=2 supersymmetric quantum field
theory, this regularization preserves by construction the manifest N=2
supersymmetry at all steps of calculating loop corrections to the effective
action. Together with N=2 supersymmetric background field method this
regularization allows to calculate quantum corrections without breaking the
manifest gauge symmetry and N=2 supersymmetry. Thus, we justify the assumption
about existence of a regularization preserving N=2 supersymmetry, which is a
key element of the N=2 non-renormalization theorem. As a result, we give the
prove of the N=2 non-renormalization theorem which does not require any
additional assumptions.Comment: 15 pages, 3 figures, 2 references added, minor corrections, accepted
for publication in Physics Letters
Harmonic N=2 Mechanics
N=2 superconformal many-body quantum mechanics in arbitrary dimensions is
governed by a single scalar prepotential which determines the bosonic potential
and the boson-fermion couplings. We present a special class of such models, for
which the bosonic potential is absent. They are classified by homogeneous
harmonic functions subject to physical symmetry requirements, such as
translation, rotation and permutation invariance. The central charge is
naturally quantized. We provide some examples for systems of identical
particles in any dimension.Comment: 1+8 page
On N=2 MQCD
We review M-theory description of 4d N=2 SQCD. Configurations of M-theory
fivebranes relevant to describe the moduli spaces of the Coulomb and Higgs
branches are studied using the Taub-NUT geometry. Minimal area membranes
related with the BPS states of N=2 SQCD are given explicitly. They almost
saturate the BPS bounds. The deviation from the bounds is due to their boundary
condition constrained by the fivebrane. The electric-magnetic duality at the
baryonic branch root is also examined from the M-theory viewpoint. In this
course, novel concepts such as creation of brane and exchange of branes in Type
II theory are explained in the framework of M-theory.Comment: 32 pages. 4 figires. Lecture in the Second Winter School on ``Branes,
Fields And Mathematical Physics" at the APCTP (Feb.9-20, 1998
N=2 superconformal nets
We provide an Operator Algebraic approach to N=2 chiral Conformal Field
Theory and set up the Noncommutative Geometric framework. Compared to the N=1
case, the structure here is much richer. There are naturally associated nets of
spectral triples and the JLO cocycles separate the Ramond sectors. We construct
the N=2 superconformal nets of von Neumann algebras in general, classify them
in the discrete series c<3, and we define and study an operator algebraic
version of the N=2 spectral flow. We prove the coset identification for the N=2
super-Virasoro nets with c<3, a key result whose equivalent in the vertex
algebra context has seemingly not been completely proved so far. Finally, the
chiral ring is discussed in terms of net representations.Comment: 42 pages. Final version to be published in Communications in
Mathematical Physic
Euclidean N=2 Supergravity
Euclidean special geometry has recently been investigated in the context of
Euclidean supersymmetric theories with vector multiplets. In the rigid case,
the scalar manifold is described by affine special para-Kahler geometry while
the target geometries of Euclidean vector multiplets coupled to supergravity
are given by projective special para-Kahler manifolds. In this letter, we
derive the Killing spinor equations of Euclidean N=2 supergravity theories
coupled to vector multiplets. These equations provide the starting point for
finding general supersymmetric instanton solutions.Comment: 12 pages, latex. Minor sign corrections in section
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