Related papers: Code subspaces for LLM geometries
We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based…
Using the AdS/CFT correspondence, we address the question of how to measure complicated space-time metrics using gauge theory probes. In particular, we consider the case of the 1/2 BPS geometries of type IIB supergravity. These geometries…
In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…
We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational…
The geometric evolution of token representations in large language models (LLMs) presents a fundamental paradox: while human language inherently organizes semantic information in low-dimensional spaces ($\sim 10^1$ dimensions), modern LLMs…
In previous work arXiv:2407.13556, we proposed an extended phase space structure at null infinity accommodating large gauge symmetries for sub$^n$-leading soft theorems in Yang-Mills, via dressing fields arising in the Stueckelberg…
Quantum field theory has successfully generated a number of general conclusions. It seems meaningful to disclose the logical forms of these conclusions. The present paper reports two results. The first result shows the logic of local gauge…
Using the recent advances in our understanding of non-perturbative aspects of type II strings we show how non-trivial exact results for $N=2$ quantum field theories can be reduced to T-dualities of string theory. This is done by…
Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field…
We consider in detail an approach (proposed by the author earlier) where quantum states are described by elements of a linear space over a Galois field, and operators of physical quantities - by linear operators in this space. The notion of…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
In the limited workspace model, we consider algorithms whose input resides in read-only memory and that use only a constant or sublinear amount of writable memory to accomplish their task. We survey recent results in computational geometry…
In harmonic superspace, the classical equations of motion of $D=4, N=2$ supersymmetric Yang-Mills theory for Minkowski and Euclidean spaces are analyzed. We study dual superfield representations of equations and subsidiary conditions…
Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the…
There is an increasing number of algorithmic computations in theoretical physics. These, while conceptually simple, can nevertheless be time-consuming and contain subtleties that should not be overlooked. Given the recent improvement of…
In 4D renormalisable theories, integrating out massive states generates in the low energy effective action higher dimensional operators (derivative or otherwise). Using a superfield language it is shown that a 4D N=1 supersymmetric theory…
The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a…
Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…