The universal Racah-Wigner symbol for U q (osp(1|2))

We propose a new and elegant formula for the Racah-Wigner symbol of selfdual continuous series of representations of U q (osp(1|2)). It describes the entire fusing matrix for both NS and R sector of N = 1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in [1]. Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the RacahWigner coefficients of finite dimensional representations

Wilson loop OPE, analytic continuation and multi-Regge limit

We explore a direct connection between the collinear limit and the multi-Regge limit for scattering amplitudes in the N $$\mathcal{N}$$ = 4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the “collinear-Regge” limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N 3 LLA and the N 4 LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE

Integrability in N=2 superconformal gauge theories

Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1|2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1|2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition

Resummations and non-perturbative corrections

We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and obtain a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling g s , we find that it includes not only the M-theoretic resummation à la Gopakumar and Vafa, but also a non-perturbative correction in g s . Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv:1306.1734 . Various other examples are also presented

Accidental inflation from Kähler uplifting

We analyze the possibility of realizing inflation with a subsequent dS vacuum in the Käahler uplifting scenario. The inclusion of several quantum corrections to the 4d effective action evades previous no-go theorems and allows for construction of simple and successful models of string inflation. The predictions of several benchmark models are in accord with current observations, i.e., a red spectral index, negligible non-gaussianity, and spectral distortions similar to the simplest models of inflation. A particularly interesting subclass of models are ``left-rolling" ones, where the overall volume of the compactified dimensions shrinks during inflation. We call this phenomenon ``inflation by deflation" (IBD), where deflation refers to the internal manifold. This subclass has the appealing features of being insensitive to initial conditions, avoiding the overshooting problem, and allowing for observable running α ∼ 0.012 and enhanced tensor-to-scalar ratio r ∼ 10−5. The latter results differ significantly from many string inflation models

Probing non-perturbative effects in M-theory

The AdS/CFT correspondence enables us to probe M-theory on various backgrounds from the corresponding dual gauge theories. Here we investigate in detail a three-dimensional U N N = 4 $$U(N)\mathcal{N}=4$$ super Yang-Mills theory coupled to one adjoint hypermultiplet and N f fundamental hypermultiplets, which is large N dual to M-theory on Ad S 4 × S 7 / ℤ N f $$Ad{S}_4\times {S}^7/{\mathrm{\mathbb{Z}}}_{N_f}$$ . Using the localization and the Fermi-gas formulation, we explore non-perturbative corrections to the partition function. As in the ABJM theory, we find that there exists a non-trivial pole cancellation mechanism, which guarantees the theory to be well-defined, between worldsheet instantons and membrane instantons for all rational (in particular, physical or integral) values of N f

Transverse momentum dependent gluon density from DIS precision data

The combined measurements of proton's structure functions in deeply inelastic scattering at the HERA collider provide high-precision data capable of constraining parton density functions over a wide range of the kinematic variables. We perform fits to these data using transverse momentum dependent QCD factorization and CCFM evolution. The results of the fits to precision measurements are used to make a determination of the nonperturbative transverse momentum dependent gluon density function, including experimental and theoretical uncertainties. We present an application of this density function to vector boson + jet production processes at the LHC

Resummed Higgs cross section at N 3 LL

We present accurate predictions for the inclusive production of a Higgs boson in proton-proton collisions, via gluon-gluon fusion. Our calculation includes nextto-next-to-leading order (NNLO) corrections in perturbative QCD, as well as the resummation of threshold-enhanced contributions to next-to-next-to-next-to-leading logarithmic (N 3 LL) accuracy, with the inclusion of the recently-determined three-loop constant coefficient (sometimes referred to as N 3 LL′ accuracy)

Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling

We study the six-point gluon scattering amplitudes in N $$\mathcal{N}$$ = 4 super Yang-Mills theory at strong coupling based on the twisted ℤ 4 -symmetric integrable model. The lattice regularization allows us to derive the associated thermodynamic Bethe ansatz (TBA) equations as well as the functional relations among the Q-/T-/Y-functions. The quantum Wronskian relation for the Q-/T-functions plays an important role in determining a series of the expansion coefficients of the T-/Y-functions around the UV limit, including the dependence on the twist parameter. Studying the CFT limit of the TBA equations, we derive the leading analytic expansion of the remainder function for the general kinematics around the limit where the dual Wilson loops become regular-polygonal. We also compare the rescaled remainder functions at strong coupling with those at two, three and four loops, and find that they are close to each other along the trajectories parameterized by the scale parameter of the integrable model

Moduli spaces in AdS 4 supergravity

We study the structure of the supersymmetric moduli spaces of $\mathcal{N}$ = 1 and $\mathcal{N}$ = 2 supergravity theories in AdS 4 backgrounds. In the $\mathcal{N}$ = 1 case, the moduli space cannot be a complex submanifold of the Kähler field space, but is instead real with respect to the inherited complex structure. In $\mathcal{N}$ = 2 supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a Kähler submanifold of the quaternionic-Kähler field space. These findings are in agreement with AdS/CFT considerations