Related papers: Code subspaces for LLM geometries
In this paper, we discuss how pure mathematics and theoretical physics can be applied to the study of language models. Using set theory and analysis, we formulate mathematically rigorous definitions of language models, and introduce the…
We study aspects of 3d $\mathcal{N}=2$ supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the…
We present a new geometrical approach to superstrings based on the geometrical theory of integration on supermanifolds. This approach provides an effective way to calculate multi-loop superstring amplitudes for arbitrary backgrounds. It…
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
((1+1)-dimensional ${\cal N}=1$ super-symmetric field theory and (3+1)-dimensional ${\cal N}=2$ super-symmetric gauge theory are discussed in a, more or less, unified way, designed to identify the quantum BPS states in both systems.…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
In four spacetime dimensions, all ${\cal N} =1$ supergravity-matter systems can be formulated in the so-called $\mathsf{U}(1)$ superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which…
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we…
We consider Abelian topological quantum field theories (TQFTs) in 3d and show that gaugings of invertible global symmetries naturally give rise to additive codes. These codes emerge as nonanomalous subgroups of the 1-form symmetry group,…
Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of…
In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…
We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic…
We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states, and give an example in which the…
We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm,…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A…