Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScheming in Dimensional Regularization
106
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time dimensions. Integrals related to the original integral by subtraction of one or more poles in dimensions other than D=4 lead to nonminimal subtraction schemes. Subtraction of all poles in correspondence with ultraviolet divergences of the loop integral leads naturally to a regularization scheme which is precisely equivalent to cutoff regularization. We therefore recover cutoff regularization from dimensional regularization with a nonminimal subtraction scheme. We then discuss the power-counting for non-relativistic effective field theories which arises in these alternative schemes.
rate research
Read More
We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the example of multi-loop banana integrals. For example, we show how Griffiths transversality, known from the theory of variation of mixed Hodge structures, leads quite generically to a set of quadratic relations among maximal cut integrals associated to Calabi-Yau motives. These quadratic relations then naturally lead to a compact expression for $l$-loop banana integrals in $D=2$ dimensions in terms of an integral over a period of a Calabi-Yau $(l-1)$-fold. This new integral representation generalizes in a natural way the known representations for $lle 3$ involving logarithms with square root arguments and iterated integrals of Eisenstein series. In a second part, we show how the results obtained by some of the authors in earlier work can be extended to dimensional regularization. We present a method to obtain the differential equations for banana integrals with an arbitrary number of loops in dimensional regularization without the need to solve integration-by-parts relations. We also present a compact formula for the leading asymptotics of banana integrals with an arbitrary number of loops in the large momentum limit. This generalizes the novel $widehat{Gamma}$-class introduced by some of the authors to dimensional regularization and provides a convenient boundary condition to solve the differential equations for the banana integrals. As an application, we present for the first time numerical results for equal-mass banana integrals with up to four loops and up to second order in the dimensional regulator.
We study how the dimensional regularization works in the light-cone gauge string field theory. We show that it is not necessary to add a contact term to the string field theory action as a counter term in this regularization at least at the tree level. We also investigate the one-loop amplitudes of the bosonic theory in noncritical dimensions and show that they are modular invariant.
We study the regularization of the codimension-2 singularities in six-dimensional Einstein-Maxwell axisymmetric models with warping. These singularities are replaced by codimension-1 branes of a ring form, situated around the axis of symmetry. We assume that there is a brane scalar field with Goldstone dynamics, which is known to generate a brane energy momentum tensor of a particular structure necessary for the above regularization to be successful. We study these compactifications in both a non-supersymmetric and a supersymmetric setting. We see that in the non-supersymmetric case, there is a restriction to the admissible warpings and furthermore to the quantum numbers of the bulk gauge field and the brane scalar field. On the contrary, in the supersymmetric case, the warping can be arbitrary.
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the translational symmetry. We then introduce a Minimal Subtraction (MS) and a Modified Minimal Subtraction (MS-Bar) scheme to renormalize the result. Finally, we consider dimensional transmutation as encountered in the case of compact extra-dimensions.
We review our recent proposals to dimensionally regularize the light-cone gauge string field theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
