arXiv subjects

Tim Meier

Publications and source records attributed to Tim Meier.

10 recordsLinked to original sources

arXiv2026

A new perspective on non-commutative deformations of field and gauge theories

We construct non-commutative deformations of field and gauge theories based on star-products implemented by Drinfel'd twists. We are able to encompass a large family of twists, including those built out of conformal symmetries and supersymmetries. The main idea behind our construction is to work with twists constructed from symmetries of the undeformed theory, that are realised as active symmetry transformations. We argue that our construction amounts to a reformulation of known deformations of gauge theories, and that it significantly extends the range of applicable examples. To ensure consistency with gauge invariance, we also identify a unimodularity condition that is weaker than the one that is normally employed in the literature, so that we can apply twists that would otherwise be left out. Finally, we also prove a planar equivalence theorem stating that the Feynman diagrams of the deformed theories retain an undeformed internal structure, with the twist acting only on their external legs. All these results are important to identify and work with deformations of $\mathcal N=4$ super Yang-Mills that are proposed to be dual to homogeneous Yang-Baxter deformations of the $AdS_5\times S^5$ superstring, but the applicability of our construction and results goes beyond that.

hep-th↗

arXiv2026

Twisting Twistor space

We construct twisted noncommutative gauge theories on twistor space and show that they are equivalent to four-dimensional twist-noncommutative gauge theories. In particular, we study twists of the Poincar\'e algebra. We explain how such a twist leads to twisted noncommutative twistor space and how to construct noncommutative versions of BF theory and holomorphic Chern-Simons theory on noncommutative supertwistor space. We show how those theories are equivalent to noncommutative versions of Yang-Mills theory and supersymmetric Yang-Mills theory, respectively.

hep-th↗

arXiv2025

Non-commutative deformations of gauge theories via Drinfel'd twists of the scale symmetry

In this paper we consider gauge theories that are relativistic and scale-invariant, and we construct their deformed versions via suitable star products. In particular, the non-commutative structure is controlled by Drinfel'd twists that are built out of symmetry generators that include the scale transformation. To achieve this, we construct a twisted differential calculus that allows us to identify the proper gauge-covariant quantities. We also show that our construction is equivalent to twists where the symmetry generators are implemented as active transformations of fields. As a consequence of our construction, the deformed gauge theories possess a twisted version of the original symmetry group. Moreover, at the planar level, the deformation is encoded just on the external legs of Feynman diagrams, leaving then the amputated diagrams undeformed. This work extends previous constructions and allows us to define twist-deformations of $\mathcal N=4$ super Yang-Mills that are conjectured to be holographically dual to a class of homogeneous Yang-Baxter deformations of $AdS_5\times S^5$.

hep-th↗

arXiv2025

Integrable spin chains in twisted maximally supersymmetric Yang-Mills theory

We study an angular dipole deformation of maximally supersymmetric Yang-Mills theory (SYM) that preserves its classical scale invariance. We show that two-point functions of suitable single trace operators, restricted to an invariant plane, are determined by scaling dimensions computable from an integrable spin chain. This spin chain is a diagonally twisted version of the famous integrable spin chain of SYM. It matches expectations from the dual string theory perfectly, presenting a precision test of holography in this new setting, and an important step to understanding general twisted integrable AdS/CFT.

hep-th↗

arXiv2023

Gauge theory on twist-noncommutative spaces

We construct actions for four dimensional noncommutative Yang-Mills theory with star-gauge symmetry, with non-constant noncommutativity, to all orders in the noncommutativity. Our construction covers all noncommutative spaces corresponding to Drinfel'd twists based on the Poincar\'e algebra, including nonabelian ones, whose $r$ matrices are unimodular. This includes particular Lie-algebraic and quadratic noncommutative structures. We prove a planar equivalence theorem for all such noncommutative field theories, and discuss how our actions realize twisted Poincar\'e symmetry, as well as twisted conformal and twisted supersymmetry, when applicable. Finally, we consider noncommutative versions of maximally supersymmetric Yang-Mills theory, conjectured to be AdS/CFT dual to certain integrable deformations of the AdS$_5\times$S$^5$ superstring.

hep-th↗

arXiv2023

Quadratic twist-noncommutative gauge theory

Studies of noncommutative gauge theory have mainly focused on noncommutative spacetimes with constant noncommutative structure, with little known about actions for noncommutative 4D Yang-Mills theory beyond this case. We construct an action for Yang-Mills theory on a quadratically-noncommutative spacetime, i.e. of quantum-plane type, obtained from a Drinfeld twist, with star-gauge symmetry. Applied to supersymmetric Yang-Mills theory, this gives a candidate AdS/CFT dual of string theory on a related deformation of AdS$_5\times$S$^5$, which is expected to be integrable in the planar limit.

hep-th↗

arXiv2022

Supersphere non-linear sigma model on the lattice

Two-dimensional $O(N)$ non-linear sigma models are exactly solvable theories and have many applications, from statistical mechanics to their use as QCD toy models. We consider a supersymmetric extension, the non-linear sigma model on the supersphere~$S^{N+2m-1|2m}\equiv \frac{OSP(N+2m|2m)}{OSP(N+2m-1|2m)}$. We briefly describe its renormalization properties and lattice discretization, and present a strategy for numerical simulations together with some preliminary numerical results.

hep-lat↗

arXiv2019

Multi-particle finite-volume effects for hexagon tessellations

Correlation functions of gauge-invariant composite operators in N=4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting resolutions of the identity involving virtual ("mirror") magnons. We consider this problem for five-point functions of protected operators. At one-loop in the 't Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem.

hep-th↗

arXiv2019

Polylogarithms from the bound state S-matrix

Higher-point functions of gauge invariant composite operators in N=4 super Yang-Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A glueing procedure welding the tiles back together is needed to return to the original object. In this note we present work in progress on n-point functions of BPS operators. In this case, quantum corrections are entirely carried by the glueing procedure. The lowest non-elementary process is the glueing of three adjacent tiles by the exchange of two single magnons. This problem has been analysed before. With a view to resolving some conceptional questions and to generalising to higher processes we are trying to develop an algorithmic approach using the representation of hypergeometric sums as integrals over Euler kernels.

hep-th↗

arXiv2018

Positivity of hexagon perturbation theory

The hexagon-form-factor program was proposed as a way to compute three- and higher-point correlation functions in $\mathcal{N}=4$ super-symmetric Yang-Mills theory and in the dual AdS$_5\times$S$^5$ superstring theory, by exploiting the integrability of the theory in the 't Hooft limit. This approach is reminiscent of the asymptotic Bethe ansatz in that it applies to a large-volume expansion. Finite-volume corrections can be incorporated through L\"uscher-like formulae, though the systematics of this expansion is largely unexplored so far. Strikingly, finite-volume corrections may feature negative powers of the 't Hooft coupling $g$ in the small-$g$ expansion, potentially leading to a breakdown of the formalism. In this work we show that the finite-volume perturbation theory for the hexagon is positive and thereby compatible with the weak-coupling expansion for arbitrary $n$-point functions.

hep-th↗