Instanton Calculus in R-R 3-form Background and Deformed N=2 Super Yang-Mills Theory

We study the ADHM construction of instantons in N=2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(-1) branes at the orbifold singularity of C^2/Z_2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(-1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the omega-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.Comment: 27 pages, version to appear in JHE

On homogeneous CR manifolds and their CR algebras

In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond to geometrical properties for the corresponding manifolds. We also give distinguished equivariant CR fibrations for homogeneous CR manifolds. In the second part of the paper we apply these results to minimal orbits for the action of a real form of a semisimple Lie group \^G on a flag manifold \^G/Q.Comment: 14 pages. AMS-LaTeX v2: minor revisio

Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction

We study an extension of the ADHM construction to give deformed anti-self-dual (ASD) instantons in N=1/2 super Yang-Mills theory with U(n) gauge group. First we extend the exterior algebra on superspace to non(anti)commutative superspace and show that the N=1/2 super Yang-Mills theory can be reformulated in a geometrical way. By using this exterior algebra, we formulate a non(anti)commutative version of the super ADHM construction and show that the curvature two-form superfields obtained by our construction do satisfy the deformed ASD equations and thus we establish the deformed super ADHM construction. We also show that the known deformed U(2) one instanton solution is obtained by this construction.Comment: 32 pages, LaTeX, v2: typos corrected, references adde

The H\"older Inequality for KMS States

We prove a H\"older inequality for KMS States, which generalises a well-known trace-inequality. Our results are based on the theory of non-commutative $L_p$-spaces.Comment: 10 page

Evaluation of juxta-apical radiolucency in cone beam CT images

OBJECTIVES: The aim of this study was to analyse the position and relationship of juxta-apical radiolucency (JAR) to the mandibular canal and buccal and/or lingual cortical plates using cone beam CT (CBCT). METHODS: A retrospective study was carried out to analyse the JAR on CBCT for 27 patients. These findings were compared with 27 age- and sex-matched patients without the presence of JAR, which acted as the control group. The CBCT images were analysed according to a checklist, to evaluate the position of the JAR and its relationship to the mandibular canal. Then, any thinning or perforation of either the buccal or lingual cortical plate due to JAR was noted, and a classification to quantify the thinning of cortical plates was proposed. The findings in the two groups were analysed using a paired comparison by McNemar test. RESULTS: A statistical increased thinning of cortical plates was seen in the JAR group compared with the control group, and most of the cases were in the J3 group. None of the patients in either the JAR or the control group showed perforation of the buccal and/or lingual cortical plate on CBCT images. CONCLUSIONS: A classification to quantify the thinning of cortical plates was proposed, which may be used for objective evaluation of the thinning of the cortical plates in future studies. The present study gives an insight into the relationship of the juxta-apical area with the mandibular canal and cortical plates in the mandible using CBCT.published_or_final_versio

Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States

We propose a deformation of ${\cal N}=4$ SYM theoery induced by nonanticommutative star product. The deformation introduces new bosonic terms which we identify with the corresponding Myers terms of a stack of D3-branes in the presence of a five-form RR flux. We take this as an indication that the deformed lagrangian describes D3-branes in such a background. The vacuum states of the theory are also examined. In a specific case where the U(1) part of the gauge field is nonvanishing the (anti)holomorphic transverse coordinates of the brane sit on a fuzzy two sphere. For a supersymmetric vacuum the antiholomorphic coordinates must necessarily commute. However, we also encounter non-supersymmetric vacua for which the antiholomorphic coordinates do not commute.Comment: 14 pages, minor changes, refs. adde