Sebastian Mizera

Extensions of Theories from Soft Limits

A bstractWe study a variety of field theories with vanishing single soft limits. In all cases, the structure of the soft limit is controlled by a larger theory, which provides an extension of the original one by adding more fields and interactions. Our main example is the U(N ) non-linear sigma model in its CHY representation. Its extension is a theory in which the NLSM Goldstone bosons interact with a cubic biadjoint scalar. Other theories we study and extend are the special Galileon and Born-Infeld theory, including its maximally supersymmetric version in four dimensions, the DBI-Volkov-Akulov theory. In all the cases, we propose the CHY representation of the complete tree-level S-matrix of the extended theories. In fact, CHY formulas are the key technique for studying the single soft limit behavior of the original theories. As a byproduct, we show that the tree-level S-matrix of the extended NLSM theory can be constructed using a very compact BCFW-like recursion relation, where physical poles are at most linear in the deformation parameter.

Decorated tensor network renormalization for lattice gauge theories and spin foam models

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.

Can scalars have asymptotic symmetries

Recently it has been understood that certain soft factorization theorems for scattering amplitudes can be written as Ward identities of new asymptotic symmetries. This relationship has been established for soft particles with spins

Spectral dimension in causal set quantum gravity

s > 0

Combinatorics and topology of Kawai-Lewellen-Tye relations

, most notably for soft gravitons and photons. Here we study the remaining case of soft scalars. We show that a class of Yukawa-type theories, where a massless scalar couples to massive particles, have an infinite number of conserved charges. This raises the question as to whether one can associate asymptotic symmetries to scalars.

Scattering Equations: Real Solutions and Particles on a Line

We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can be connected to the nonlocality of causal set theory that is deeply rooted in its fundamentally Lorentzian nature. Based on its large-scale behaviour, we conjecture that the spectral dimension can serve as a tool to distinguish causal sets that approximate manifolds from those that do not. As a new tool to probe quantum spacetime in different quantum gravity approaches, we introduce a novel dimensional estimator, the causal spectral dimension, based on the meeting probability of two random walkers, which respect the causal structure of the quantum spacetime. We discuss a causal-set example, where the spectral dimension and the causal spectral dimension differ, due to the existence of a preferred foliation.

Multi-colour detection of gravitational arcs

A bstractWe revisit the relations between open and closed string scattering amplitudes discovered by Kawai, Lewellen, and Tye (KLT). We show that they emerge from the un-derlying algebro-topological identities known as the twisted period relations. In order to do so, we formulate tree-level string theory amplitudes in the language of twisted de Rham theory. There, open string amplitudes are understood as pairings between twisted cycles and cocycles. Similarly, closed string amplitudes are given as a pairing between two twisted cocycles. Finally, objects relating the two types of string amplitudes are the α′-corrected bi-adjoint scalar amplitudes recently defined by the author [1]. We show that they naturally arise as intersection numbers of twisted cycles. In this work we focus on the combinatorial and topological description of twisted cycles relevant for string theory amplitudes. In this setting, each twisted cycle is a polytope, known in combinatorics as the associahedron, together with an additional structure encoding monodromy properties of string integrals. In fact, this additional structure is given by higher-dimensional generalizations of the Pochhammer contour. An open string amplitude is then computed as an integral of a logarithmic form over an associahedron. We show that the inverse of the KLT kernel can be calculated from the knowledge of how pairs of associahedra intersect one another in the moduli space. In the field theory limit, contributions from these intersections localize to vertices of the associahedra, giving rise to the bi-adjoint scalar partial amplitudes.

Scattering Amplitudes from Intersection Theory

A bstractWe find n(n − 3)/2-dimensional regions of the space of kinematic invariants, where all the solutions to the scattering equations (the core of the CHY formulation of amplitudes) for n massless particles are real. On these regions, the scattering equations are equivalent to the problem of finding stationary points of n − 3 mutually repelling particles on a finite real interval with appropriate boundary conditions. This identification directly implies that for each of the (n − 3)! possible orderings of the n − 3 particles on the interval, there exists one stable stationary point. Furthermore, restricting to four dimensions, we find that the separation of the solutions into k ∈ {2, 3, . . . , n − 2} sectors naturally matches that of permutations of n − 3 labels into those with k − 2 descents. This leads to a physical realization of the combinatorial meaning of the Eulerian numbers.

CHY Loop Integrands from Holomorphic Forms

Strong gravitational lensing provides fundamental insights into the understanding of the dark matter distribution in massive galaxies, galaxy clusters, and the background cosmology. Despite their importance, few gravitational arcs have been discovered so far. The urge for more complete, large samples and unbiased methods of selecting candidates increases. Several methods for the automatic detection of arcs have been proposed in the literature, but large amounts of spurious detections retrieved by these methods force observers to visually inspect thousands of candidates per square degree to clean the samples. This approach is largely subjective and requires a huge amount of checking by eye, especially considering the actual and upcoming wide-field surveys, which will cover thousands of square degrees. In this paper we study the statistical properties of the colours of gravitational arcs detected in the 37 deg 2 of the CFHTLS-Archive-Research Survey (CARS). Most of them lie in a relatively small region of the (g � − r � ,r � − i � ) colour–colour diagram. To explain this property, we provide a model that includes the lensing optical depth expected in a ΛCDM cosmology that, in combination with the sources’ redshift distribution of a given survey, in our case CARS, peaks for sources at redshift z ∼ 1. By furthermore modelling the colours derived from the spectral energy distribution of the galaxies that dominate the population at that redshift, the model reproduces the observed colours well. By taking advantage of the colour selection suggested by both data and model, we automatically detected 24 objects out of 90 detected by eye checking. Compared with the single-band arcfinder, this multiband filtering returns a sample complete to 83% and a contamination reduced by a factor of ∼6.5. New gravitational arc candidates are also proposed.Strong gravitational lensing provides fundamental insights in the understanding of the dark matter distribution in massive galaxies, galaxy clusters and the background cosmology. Despite their importance, the number of gravitational arcs discovered so far is small. The urge for more complete, large samples and unbiased methods of selecting candidates is rising. A number of methods for the automatic detection of arcs have been proposed in the literature, but large amounts of spurious detections retrieved by these methods forces observers to visually inspect thousands of candidates per square degree in order to clean the samples. This approach is largely subjective and requires a huge amount of eye-ball checking, especially considering the actual and upcoming wide field surveys, which will cover thousands of square degrees. In this paper we study the statistical properties of colors of gravitational arcs. We found that most of them lie in a relatively small region of the color-color diagram (g 0 r 0 ; r 0 i 0 ). We support this observational evidence by studying lensing cross section, which peaks for sources at redshift z 1, where the source-galaxy population is dominated by galaxies with large star forming regions and hence well defined colors. The use of this distinctive feature, in combination with an automatic arcfinder, reduces sample contamination by a factor of 6 7. We tested the performance of the method against 37 deg 2 of the CARS survey, detecting 73 new arc candidates.

Inverse of the string theory KLT kernel

We use Picard-Lefschetz theory to prove a new formula for intersection numbers of twisted cocycles associated with a given arrangement of hyperplanes. In a special case when this arrangement produces the moduli space of punctured Riemann spheres, intersection numbers become tree-level scattering amplitudes of quantum field theories in the Cachazo-He-Yuan formulation.