We study the duality between color and kinematics for Sudakov form factors of ${\rm tr}(F^2)$ in non-supersymmetric pure Yang-Mills theory. construct integrands that manifest color-kinematics up to two loops. The resulting numerators are given terms Lorentz products momenta polarization vectors, which have same powers loop as from Feynman rules. checked by $d$-dimensional unitarity cuts valid a...

A bstract We address a longstanding question of whether ABJM theory has Wilson loop operators preserving eight supercharges (so 1/3 BPS). present such loops made large supermatrix combining two 1/2 BPS loops. study the spectrum operator insertions into them including displacement and several others their correlation functions. Another natural construction arising in this context are with altern...

Symbolic execution is a successful and very popular technique used in software verification and testing. A key limitation of symbolic execution is in dealing with code containing loops. The problem is that even a single loop can generate a huge number of different symbolic execution paths, corresponding to different number of loop iterations and taking various paths through the loop. We introdu...

We describe how Gröbner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Gröbner-type bases associated with polynomials of shift operators...

We present a 4-dimensional nonsupersymmetric black hole solution to low energy type IIA string theory which carries D0and D6-brane charges. For equal charges this solution reduces to the one discussed recently by Sheinblatt. We construct the corresponding brane configuration for the extremal case and compute the 1-loop matrix theory potential for the scattering of a 0-brane probe off this brane...

We use closed geodesics to construct and compute Botttype Morse homology groups for the energy functional on the loop space of flat n-dimensional tori, n ≥ 1, and Bott-type Floer cohomology groups for their cotangent bundles equipped with the natural symplectic structure. Both objects are isomorpic to the singular homology of the loop space. In an appendix we perturb the equations in order to e...

In this paper, we first modify the Smart-Vercauteren’s fully homomorphic encryption scheme [SV10] by applying self-loop bootstrappable technique. The security of the modified scheme only depends on the hardness of the polynomial coset problem, removing the assumption of the sparse subset sum problem in the original paper in [SV10]. Moreover, we construct a non-self-loop in FHE by using cycle ke...

By considering scalar theories on the fuzzy sphere as matrix models, we construct a renormalization scheme and calculate the one-loop effective action. Because of UVIR mixing, the twoand the four-point correlators at low energy are not slowly varying functions of external momenta. Interestingly, we also find that field theories on fuzzy RP2 avoid UV-IR mixing and hence are much more like conven...