Twisty itsy bitsy topological field theory

We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on those surfaces respecting signs (sutures). It has information-theoretic (``itsy'') and quantum-field-theoretic (``bitsy'') aspects. In the process we extend some results of sutured Floer homology, consider associated ribbon graph structures, and construct explicit admissible Heegaard decompositions.Comment: 52 pages, 26 figure

Sutured Floer homology, sutured TQFT and non-commutative QFT

We define a "sutured topological quantum field theory", motivated by the study of sutured Floer homology of product 3-manifolds, and contact elements. We study a rich algebraic structure of suture elements in sutured TQFT, showing that it corresponds to contact elements in sutured Floer homology. We use this approach to make computations of contact elements in sutured Floer homology over $\Z$ of sutured manifolds $(D^2 \times S^1, F \times S^1)$ where $F$ is finite. This generalises previous results of the author over $\Z_2$ coefficients. Our approach elaborates upon the quantum field theoretic aspects of sutured Floer homology, building a non-commutative Fock space, together with a bilinear form deriving from a certain combinatorial partial order; we show that the sutured TQFT of discs is isomorphic to this Fock space.Comment: v.2: 49 pages, 13 figures. Improved and expanded exposition, some minor corrections. Sections on torsion, annuli, and tori moved to a separate pape

Next-to-Next-to-Leading Order QCD Corrections in Models of TeV-Scale Gravity

We compute the next-to-next-to-leading order QCD corrections to the graviton production in models of TeV-scale gravity, within the soft-virtual approximation. For the Arkani-Hamed, Dimopoulos and Dvali (ADD) model we evaluate the contribution to the Drell-Yan cross section, and we present distributions for the di-lepton invariant mass at the LHC with a center-of-mass energy $\sqrt{s_H}=14\text{TeV}$. We find a large $K$ factor ($K\simeq 1.8$) for large values of invariant mass, which is the region where the ADD graviton contribution dominates the cross section. The increase in the cross section with respect to the previous order result is larger than $10\%$ in the same invariant mass region. We also observe a substantial reduction in the scale uncertainty. For the Randall-Sundrum (RS) model we computed the total single graviton production cross section at the LHC. We find an increase between $10\%$ and $13\%$ with respect to the next-to-leading order prediction, depending on the model parameters. We provide an analytic expression for the NNLO $K$ factor as a function of the lightest RS graviton mass.Comment: 16 pages, 7 figure