XXVI DAE-BRNS High Energy Physics Symposium 2024

Supersymmetry and Quantum Phase Transition in a matrix model of SU(2) gauge theory

Not scheduled

20m

Swatantrata Bhavan, Banaras Hindu University, Varanasi

Oral Formal theory

Speaker

ARKAJYOTI BANDYOPADHYAY (Indian Institute of Technology, Bhubaneswar)

Description

For decades supersymmetric matrix models of $SU(N)$ gauge theories has been a subject of particular interest. We consider a matrix model of $SU(2)$ gauge theory coupled with a Weyl fermion transforming in the adjoint representation of the gauge group. This model depicts $\mathcal{N}=1$ SUSY with anomalous global $U(1{)}_R$ symmetry. The matrix model, being quantum mechanical, provides a simplified computational platform to study the properties of the system in both weak and strong coupling regimes ($g$ is the dimensionless Yang-Mills coupling constant). Here, we use a Rayleigh-Ritz variational technique to diagonalize the Hamiltonian and construct the color-singlet spin-0 and spin-1/2 energy eigenstates. In the weak coupling regime ($0

In the extreme strong coupling regime (i.e. $g=\mathrm{\infty }$), the classical potential has flat directions and the spectrum of the quantum Hamiltonian is expected to be continuous. In our numerical work with finite bosonic cut-off $N_{max}$ in the varitational ansatz, we find that the energy eigenvalues at $g=\mathrm{\infty }$ has power-law dependence on $N_{max}$. This is a signature of the emerging continuous spectrum.

For $1\ll g<\mathrm{\infty }$, the numerical error due to the finite cut-off shows a power-law behavior on $N_{max}$ and in this case, the spectrum remains discrete. However, here the degeneracy between the superpartners is lifted. This corresponds to a crossover from the supersymmetric weak coupling phase to a SUSY-broken strong coupling phase (with possibility of SUSY being restored only at $g=\mathrm{\infty }$).

Presentation materials

SUSY_DAE_HEP.pdf