Search results for "hep-th"
showing 10 items of 757 documents
A novel approach to integration by parts reduction
2015
Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on Laporta's algorithm. The key idea is to construct algebraic identities from numerical samples obtained from reductions over finite fields. We expect the method to be highly amenable to parallelization, show a low memory footprint during the reduction step, and allow for significantly better run-times.
Stability and physical properties of spherical excited scalar boson stars
2023
We study the time evolution of spherical, excited -- with $n$ radial nodes -- scalar boson stars in General Relativity minimally coupled to a complex massive scalar field with quartic self-interactions. We report that these stars, with up to $n=10$, can be made dynamically stable, up to timescales of $t\sim\frac{10^{4}}{c\mu}$, where $\mu$ is the inverse Compton wavelength of the scalar particle, for sufficiently large values of the self-interactions coupling constant $\lambda$, which depend on $n$. We observe that the compactness of these solutions is rather insensitive to $n$, for large $\lambda$ and fixed frequency. Generically, along the branches where stability was studied, these excit…
Fundamental physics with high-energy cosmic neutrinos today and in the future
2019
The astrophysical neutrinos discovered by IceCube have the highest detected neutrino energies --- from TeV to PeV --- and likely travel the longest distances --- up to a few Gpc, the size of the observable Universe. These features make them naturally attractive probes of fundamental particle-physics properties, possibly tiny in size, at energy scales unreachable by any other means. The decades before the IceCube discovery saw many proposals of particle-physics studies in this direction. Today, those proposals have become a reality, in spite of astrophysical unknowns. We will showcase examples of doing fundamental neutrino physics at these scales, including some of the most stringent tests o…
Spontaneous Scalarization of Charged Black Holes
2018
Extended scalar-tensor-Gauss-Bonnet (eSTGB) gravity has been recently argued to exhibit spontaneous scalarisation of vacuum black holes (BHs). A similar phenomenon can be expected in a larger class of models, which includes e.g. Einstein-Maxwell-scalar (EMS) models, where spontaneous scalarisation of electrovacuum BHs should occur. EMS models have no higher curvature corrections, a technical simplification over eSTGB models that allows us to investigate, fully non-linearly, BH scalarisation in two novel directions. Firstly, numerical simulations in spherical symmetry show, dynamically, that Reissner-Nordstr\"om (RN) BHs evolve into a perturbatively stable scalarised BH. Secondly, we compute…
Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
2017
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to $\varepsilon$-form.
Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD
2015
Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.
Matter Dependence of the Four-Loop Cusp Anomalous Dimension
2019
We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop light-like cusp anomalous dimension in QCD, with $n_f$ fermion and $n_s$ scalar flavours. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end we first identify a set of integrals whose integrands have a dlog form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals w…
N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant
1991
We discuss gauge theory with a topological N=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space $\cal M$ and the partition function equals the Euler number of $\cal M$. We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of…
Weight Systems from Feynman Diagrams
1996
We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful association of renormalization theory with knot theory.
A Comparison between Star Products on Regular Orbits of Compact Lie Groups
2001
In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure.