Related papers: Generating Functionals for Spin Foam Amplitudes

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

We present an off-shell generating function for all cubic interactions of Higher Spin gauge fields constructed in arXiv:1003.2877. It is a generalization of the on-shell generating function proposed in arXiv:1006.5242, is written in a very…

This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a…

A method for determining the generalised scaling function(s) arising in the high spin behaviour of long operator anomalous dimensions in the planar $sl(2)$ sector of ${\cal N}=4$ SYM is proposed. The all-order perturbative expansion around…

We show that 10D spinor helicity formalism can be understood as spinor moving frame approach to supersymmetric particles extended to the description of amplitudes. This allows us to develop the spinor helicity formalism for 11D supergravity…

We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results…

This paper is the second of two which construct coherent states for spin networks with planar symmetry. Paper 1 constructs set of coherent states peaked at specific values of holonomy and triad. These operators acting on the coherent state…

The purely on-shell approach to effective field theories requires the construction of independent contact terms. Employing the little-group-covariant massive-spinor formalism, we present the first systematic derivation of independent…

One-dimensional spinor gases with strong delta interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom…

The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational…

It is a classical result due to Jacobi in algebraic combinatorics that the generating function of closed walks at a vertex $u$ in a graph $G$ is determined by the rational function \[ \frac{\phi_{G-u}(t)}{\phi_G(t)} \] where $\phi_G(t)$ is…

We study independent sets in strong powers of circulant graphs using a transfer matrix formulation. The compatibility constraints separate into intra-layer and inter-layer components, yielding a transfer operator that is equivariant under…

Working over an algebraically closed base field $k$ of characteristic 2, the ring of invariants $R^G$ is studied, where $G$ is the orthogonal group O(n) or the special orthogonal group SO(n), acting naturally on the coordinate ring $R$ of…

We study the four-gluon scattering amplitude in the high energy limit of QCD written in terms of its conformal expansion. We highlight the need to include both even and odd conformal spin contributions in order to map it to an iterative…

A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…

We carry out a systematic study of primary operators in the conformal field theory of a free Weyl fermion. Using SO(4,2) characters we develop counting formulas for primaries constructed using a fixed number of fermion fields. By…

The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure…

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…

We study the dynamics of supervised on-line learning of realizable tasks in feed-forward neural networks. We focus on the regime where the number of examples used for training is proportional to the number of input channels N. Using…

We consider "gauge invariant" operators in Sym^N T^4, the symmetric product orbifold of N copies of the 2d supersymmetric sigma model with T^4 target. We discuss a spin chain representation for single-cycle operators and study their two…