SUPER_QUANTA
Supersymmetric Quantum Field Theories and Software Development for the Lattice Formulation
Project Summary:
SUPER_QUANTA aims to enhance analytical computations in Quantum Field Theories (QFTs),
studying interactions among quarks, gluons, and their superpartners. It focuses on
models which are forerunners to supersymmetric extensions of the Standard Model and
provides mechanisms for new Beyond-the-Standard-Model Physics.
In four-dimensional N=1 Supersymmetric Yang-Mills (SYM) theories, SUPER_QUANTA will
investigate the "current" supermultiplet, consisting of the Noether Supercurrent
operator, the axial current, and the Energy-Momentum tensor, using improved
discretizations and stout smearing on the lattice. Advanced perturbative methods will be
employed to disentangle operator mixing due to quantum corrections. Furthermore, the
project will utilize a coordinate-space Gauge-Invariant Renormalization Scheme (GIRS) to
explore Green's functions of Noether currents within the Wess-Zumino gauge.
In addition, the project aims to determine all fine-tunings and counterterms on the
lattice using the overlap fermion action to simulate specific Supersymmetric (SUSY)
models, including Supersymmetric QCD. This will facilitate quantitative investigations
of phase structures, transitions, chiral symmetry, and SUSY violation phenomena on the
lattice. To this end, several two-, three-, and four-point Green's functions must be
computed at one-loop order; from these Green's functions, the renormalization of all
fields, masses, and couplings on the lattice will be determined.
Lastly, the project will develop user-friendly software to improve multi-loop Feynman
diagram calculations on the lattice, incorporating Graph Theory and chirally invariant
lattice actions. This project will also adapt a compression tool to reduce the storage
space of data coming from the calculation of Feynman diagrams, as well as simulation
data.
Details:
| Programme | EXCELLENCE HUBS |
|---|---|
| Proposal Number | EXCELLENCE/0524/0208 |
| Proposal Acronym | SUPER_QUANTA |
| Funding | 
The project is implemented under the programme of social cohesion “THALIA 2021- 2027” co-funded by the European Union, through Research and Innovation Foundation. |
Paper: N = 1 supersymmetric QCD on the lattice using overlap fermions
Using N ¼ 1 supersymmetric QCD (SQCD) as a prototype model, this work presents a formulation of overlap quarks and gluinos on the lattice, with particular emphasis on the construction of chirally symmetric Yukawa terms. By incorporating the Ginsparg-Wilson relation, chiral transformations, and the Majorana condition for gluinos, we construct a consistent framework that preserves a lattice-modified chiral symmetry and reduces the number of required counterterms compared to Wilson-type discretizations. The formulation introduces auxiliary fermionic fields to realize exact chiral symmetry in Yukawa interactions and enables a detailed analysis of the resulting matrix structures. Upon functionally integrating out the auxiliary fields, ultralocal interaction terms emerge as new contributions to the lattice action. This approach provides a robust foundation for nonperturbative lattice studies of supersymmetric gauge theories. Future work will focus on computing all perturbative fine-tunings required in this formulation to enable continuum matching and numerical simulations of SQCD.