Interplay between Background Fluxes and Instanton Configurations

We focus on D-brane models in presence of closed string background fluxes. These fluxes modify the effective interactions on Dirichlet and Euclidean branes, in particular inducing fermionic masses. We show how they can create new non-perturbative superpotential terms in presence of gauge and exotic instantons in SQCD-like models.Comment: 18 pages. To appear in Nuovo Cimento B for the INFN "Sergio Fubini Prize" 200

Transmuting CHY formulae

© The Author(s) 2019.The various formulations of scattering amplitudes presented in recent years have underlined a hidden unity among very different theories. The KLT and BCJ relations, together with the CHY formulation, connect the S-matrices of a wide range of theories: the transmutation operators, recently proposed by Cheung, Shen and Wen, provide an account for these similarities. In this note we use the transmutation operators to link the various CHY integrands at tree-level. Starting from gravity, we generate the integrands for YangMills, biadjoint scalar, Einstein-Maxwell, Yang-Mills scalar, Born-Infeld, Dirac-Born-Infeld, non-linear sigma model and special Galileon theories, as well as for their extensions. We also commence the study of the CHY-like formulae at loop level.Peer reviewe

Applications of String Theory: Non-perturbative Effects in Flux Compactifications and Effective Description of Statistical Systems

In this paper, which is a revised version of the author's PhD thesis, we analyze two different applications of string theory. In the first part, we focus on four dimensional compactifications of Type II string theories preserving N=1 supersymmetry, in presence of intersecting or magnetized D-branes. We show, through world-sheet methods, how the insertion of closed string background fluxes may modify the effective interactions on Dirichlet and Euclidean branes. In particular, we compute flux-induced fermionic masses. The generality of our results is exploited to determine the soft terms of the action on the instanton moduli space. Finally, we investigate how fluxes create new non-perturbative superpotential terms in presence of gauge and stringy instantons in SQCD-like models. The second part is devoted to the description of statistical systems through effective string models. In particular, we focus our attention on (d-1)-dimensional interfaces, present in particular statistical systems defined on compact d-dimensional spaces. We compute their exact partition function by resorting to standard covariant quantization of the Nambu-Goto theory, and we compare it with Monte Carlo data. Then, we propose an effective model to describe interfaces in 2d space and test it against the dimensional reduction of the Nambu-Goto description of the 2d interface.Comment: 159 pages, PhD thesi

The Loop Momentum Amplituhedron

In this paper we focus on scattering amplitudes in maximally supersymmetric Yang-Mills theory and define a long sought-after geometry, the loop momentum amplituhedron, which we conjecture to encode tree and (the integrands of) loop amplitudes in spinor helicity variables. Motivated by the structure of amplitude singularities, we define an extended positive space, which enhances the Grassmannian space featuring at tree level, and a map which associates to each of its points tree-level kinematic variables and loop momenta. The image of this map is the loop momentum amplituhedron. Importantly, our formulation provides a global definition of the loop momenta. We conjecture that for all multiplicities and helicity sectors, there exists a canonical logarithmic differential form defined on this space, and provide its explicit form in a few examples.Comment: 17 pages, 1 figur

Amplituhedra, and Beyond

© 2020 The Author(s). Published by IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence (https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. These pertain to a broader family of geometries called positive geometries, whose basics we review. We also describe other members of this family that are associated with different physical quantities and briefly consider the most recent developments related to positive geometries. Finally, we discuss the main open problems in the field. This is a Topical Review invited by Journal of Physics A: Mathematical and Theoretical.Peer reviewe

The Grassmannian for celestial superamplitudes

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), https://creativecommons.org/licenses/by/4.0/Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in N = 4 super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries.Peer reviewedFinal Published versio

Kleiss-Kuijf relations from momentum amplituhedron geometry

44 pages, 19 figuresAbstract: In recent years, it has been understood that color-ordered scattering amplitudes can be encoded as logarithmic differential forms on positive geometries. In particular, amplitudes in maximally supersymmetric Yang-Mills theory in spinor helicity space are governed by the momentum amplituhedron. Due to the group-theoretic structure underlying color decompositions, color-ordered amplitudes enjoy various identities which relate different orderings. In this paper, we show how the Kleiss-Kuijf relations arise from the geometry of the momentum amplituhedron. We also show how similar relations can be realised for the kinematic associahedron, which is the positive geometry of bi-adjoint scalar cubic theory.Peer reviewe

Prescriptive Unitarity from Positive Geometries

© The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/In this paper, we define the momentum amplituhedron in the four-dimensional split-signature space of dual momenta. It encodes scattering amplitudes at tree level and loop integrands for N=4 super Yang-Mills in the planar sector. In this description, every point in the tree-level geometry is specified by a null polygon. Using the null structure of this kinematic space, we find a geometry whose canonical differential form produces loop-amplitude integrands. Remarkably, at one loop it is a curvy version of a simple polytope, whose vertices are specified by maximal cuts of the amplitude. This construction allows us to find novel formulae for the one-loop integrands for amplitudes with any multiplicity and helicity. The formulae obtained in this way agree with the ones derived via prescriptive unitarity. It makes prescriptive unitarity naturally emerge from this geometric description.Peer reviewe

Prescriptive Unitarity from Positive Geometries

In this paper, we define the momentum amplituhedron in the four-dimensional split-signature space of dual momenta. It encodes scattering amplitudes at tree level and loop integrands for N=4 super Yang-Mills in the planar sector. In this description, every point in the tree-level geometry is specified by a null polygon. Using the null structure of this kinematic space, we find a geometry whose canonical differential form produces loop-amplitude integrands. Remarkably, at one loop it is a curvy version of a simple polytope, whose vertices are specified by maximal cuts of the amplitude. This construction allows us to find novel formulae for the one-loop integrands for amplitudes with any multiplicity and helicity. The formulae obtained in this way agree with the ones derived via prescriptive unitarity. It makes prescriptive unitarity naturally emerge from this geometric description.Comment: 41 pages, 23 figure

Amplituhedron meets Jeffrey-Kirwan Residue

The tree amplituhedra A^(m)_n,k are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for m=4 as a geometric construction encoding tree-level scattering amplitudes in planar N=4 super Yang-Mills theory, they are mathematically interesting for any m. In this paper we strengthen the relation between scattering amplitudes and geometry by linking the amplituhedron to the Jeffrey-Kirwan residue, a powerful concept in symplectic and algebraic geometry. We focus on a particular class of amplituhedra in any dimension, namely cyclic polytopes, and their even-dimensional conjugates. We show how the Jeffrey-Kirwan residue prescription allows to extract the correct amplituhedron volume functions in all these cases. Notably, this also naturally exposes the rich combinatorial and geometric structures of amplituhedra, such as their regular triangulations.Peer reviewedFinal Accepted Versio