SU(2)xU(1) non-anticommutative N=2 supersymmetric gauge theory

We derive the master function governing the component action of the four-dimensional non-anticommutative (NAC) and fully N=2 supersymmetric gauge field theory with a non-simple gauge group U(2)=SU(2)xU(1). We use a Lorentz singlet NAC-deformation parameter and an N=2 supersymmetric star (Moyal) product which do not break any of the fundamental symmetries of the undeformed N=2 gauge theory. The scalar potential in the NAC-deformed theory is calculated. We also propose the non-abelian BPS-type equations in the case of the NAC-deformed N=2 gauge theory with the SU(2) gauge group, and comment on the SU(3) case too. The NAC-deformed field theories can be thought of as the effective (non-perturbative) N=2 gauge field theories in a certain (scalar only) N=2 supergravity background.Comment: 16 pages, 1 figure, LaTeX; a few references adde

Gravity in spacetimes with cosmological constants

This thesis is composed of two parts: gravity in the spacetime with a negative/positive cosmological constant. The first part, which is the negative case, devotes to constructing the IIB supergravity dual solution in AdS/CFT correspondence for N = (1, 0) and N = (1/2, 0) non-anticommutative deformed super Yang-Mills theory. The non-anticommutativity is realised on N D3-branes in certain constant self-dual RR 5-form background fields. These background fields can be sourced by a set of additional D3-branes intersecting the N D3's. By taking the near horizon limit to the brane configurations, the supergravity solutions are obtained. The mapping between the bulk scalar fields and the boundary operators for N = (1, 0) case is investigated, and it is found that the spectrum of a particular class of the BPS operators is not deformed by the non-anticommutativity. The second part is for the positive cosmological constant case. In this part, a black fusiform solution with appositive cosmological const in d =5, N = 4 de Sitter supergravity is constructed. The solution is obtained via the braneworld Kaluza-Klein reduction ansatz, and preserves half of the de Sitter supersymmetry. It is static, with the gravitational contraction being balanced by the cosmological repulsion. The black fusiform has an event horizon and a cosmological horizon, and is asymptotically non-de Sitter. The horizons are of an in x S(^2) topology, and contain singularities at the opposite ends due to the nature of the reduction ansatz. Despite the singularities, the solution exhibits some physically properties compatible with that of the regular asymptotically de Sitter spacetimes. The entropy and mass observe the N-bound proposal and the maximal mass conjecture respectively. It also carries a charge which contributes to the 1st law of black hole mechanics

Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory

In this thesis, we report on results in non-anticommutative field theory and twistor string theory, trying to be self-contained. We first review the construction of non-anticommutative N=4 super Yang-Mills theory and discuss a Drinfeld-twist which allows to regain a twisted supersymmetry in the non-anticommutative setting. This symmetry then leads to twisted chiral rings and supersymmetric Ward-Takahashi identities, which, when combined with the usual naturalness argument by Seiberg, could yield non-renormalization theorems for non-anticommutative field theories. The major part of this thesis consists of a discussion of various geometric aspects of the Penrose-Ward transform. We present in detail the case of N=4 super Yang-Mills theory and its self-dual truncation. Furthermore, we study reductions of the supertwistor space to exotic supermanifolds having even nilpotent dimensions as well as dimensional reductions to mini-supertwistor and mini-superambitwistor spaces. Eventually, we present two pairs of matrix models in the context of twistor string theory, and find a relation between the ADHM- and Nahm-constructions and topological D-brane configurations.Comment: PhD thesis, 280 pages, 9 figure

Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface terms

We calculate the one-loop quantum corrections to the mass and central charge of N=2 and N=4 supersymmetric monopoles in 3+1 dimensions. The corrections to the N=2 central charge are finite and due to an anomaly in the conformal central charge current, but they cancel for the N=4 monopole. For the quantum corrections to the mass we start with the integral over the expectation value of the Hamiltonian density, which we show to consist of a bulk contribution which is given by the familiar sum over zero-point energies, as well as surface terms which contribute nontrivially in the monopole sector. The bulk contribution is evaluated through index theorems and found to be nonvanishing only in the N=2 case. The contributions from the surface terms in the Hamiltonian are cancelled by infinite composite operator counterterms in the N=4 case, forming a multiplet of improvement terms. These counterterms are also needed for the renormalization of the central charge. However, in the N=2 case they cancel, and both the improved and the unimproved current multiplet are finite.Comment: 1+40 pages, JHEP style. v2: small corrections and additions, references adde

Comments on the relation of M-theory and supergravity

M-theory was synthesized in 1995 due to observations regarding an intricate web-of-dualities that relate the five superstring theories, and recognition that D=11 supergravity is both nonperturbatively dual to type-IIA superstring and the low-energy limit of an 11-dimensional theory. Mutual development of M-theory and supergravity ensued. During the past three years, related but independent field theory calculations suggest that N=8 d=4 supergravity scattering amplitudes may be ultraviolet finite. Since supergravity theories represent the low-energy effective actions of string theories and describe the interaction of massless fields in the string theory spectrum, it is noteworthy that it was suggested recently that N=8 supergravity, in the event stringy states are discarded, is inconsistent and thus in the Swampland. This thesis proposes a different interpretation based on results that integrate BPS-soliton states and strengthen the symbiotic relationship between N=8 supergravity and M-theory, which would lead to mutual development

Non-perturbative methods in non-linear field theories and their supersymmetric extensions

We collect the main results obtained along this Ph.D. thesis: \Non-perturbative methods in non-linear eld theories and their supersymmetric extensions". The rst original presentation for K eld theories is performed in chapter 7. We proposed a simpler supersymmetric extension of such theories. With this extension it is easy to calculate supersymmetric charges, and therefore all the supersymmetric algebra is found. Nevertheless, in the last section we demonstrate that with this oversimpli ed scheme of supersymmetrization the model contains ghosts