Counting chiral primaries in N=1 d=4 superconformal field theories

I derive a procedure to count chiral primary states in N=1 superconformal field theories in four dimensions. The chiral primaries are counted by putting the N=1 field theory on S^3 X R. I also define an index that counts semi-short multiplets of the superconformal theory. I construct N=1 supersymmetric Lagrangians on S^3 X R for theories which are believed to flow to a conformal fixed point in the IR. For ungauged theories I reduce the field theory to a supersymmetric quantum mechanics, whereas for gauge theories I use chiral ring arguments. I count chiral primaries for SU(2) SYM with three flavors and its Seiberg dual. Those two results agree provided a new chiral ring relation holds.Comment: 34 pages, significant revisio

Closed-form two-loop Euler-Heisenberg Lagrangian in a self-dual background

We show that the two-loop Euler-Heisenberg effective Lagrangian for scalar QED in a constant Euclidean self-dual background has a simple explicit closed form expression in terms of the digamma function. This result leads to a simple analysis of the weak- and strong-field expansions, the two-loop scalar QED beta function, and the analytic continuation properties of the effective Lagrangian and its imaginary part.Comment: 8 pages, late

FLT3 mutations in Early T-Cell Precursor ALL characterize a stem cell like leukemia and imply the clinical use of tyrosine kinase inhibitors

Early T-cell precursor acute lymphoblastic leukemia (ETP-ALL) has been identified as high-risk subgroup of acute T-lymphoblastic leukemia (T-ALL) with a high rate of FLT3-mutations in adults. To unravel the underlying pathomechanisms and the clinical course we assessed molecular alterations and clinical characteristics in a large cohort of ETP-ALL (n = 68) in comparison to non-ETP T-ALL adult patients. Interestingly, we found a high rate of FLT3-mutations in ETP-ALL samples (n = 24, 35%). Furthermore, FLT3 mutated ETP-ALL was characterized by a specific immunophenotype (CD2+/CD5-/CD13+/CD33-), a distinct gene expression pattern (aberrant expression of IGFBP7, WT1, GATA3) and mutational status (absence of NOTCH1 mutations and a low frequency, 21%, of clonal TCR rearrangements). The observed low GATA3 expression and high WT1 expression in combination with lack of NOTCH1 mutations and a low rate of TCR rearrangements point to a leukemic transformation at the pluripotent prothymocyte stage in FLT3 mutated ETP-ALL. The clinical outcome in ETP-ALL patients was poor, but encouraging in those patients with allogeneic stem cell transplantation (3-year OS: 74%). To further explore the efficacy of targeted therapies, we demonstrate that T-ALL cell lines transfected with FLT3 expression constructs were particularly sensitive to tyrosine kinase inhibitors. In conclusion, FLT3 mutated ETP-ALL defines a molecular distinct stem cell like leukemic subtype. These data warrant clinical studies with the implementation of FLT3 inhibitors in addition to early allogeneic stem cell transplantation for this high risk subgroup

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste