Abstract

I study finite-temperature $\mathcal N=1$ super Yang-Mills for any gauge group $G=A_N, B_N, C_N, D_N, E_{6,7,8},F_4,G_2$, compactified from four dimensions on a torus, $\mathbb R^2\times S^1_L\times S^1_{\beta}$. I examine in particular the low temperature regime $L\ll\beta=1/T$, where $L$ is the length of the spatial circle with periodic boundary conditions and with anti-periodic boundary conditions for the adjoint gauginos along the thermal cycle $S^1_{\beta}$. For small such $L$ we are in a regime were semiclassical calculations can be performed and a transition occurs at $T_c$ much smaller than $1/NL$. The transition is mediated by the competition between non-perturbative objects including 'exotic' topological molecules: neutral and magnetic bions composed of BPS and KK monopole constituents, with $r=rank(G)$ different charges in the co-root lattice of the gauge group $G$, and the perturbative electrically charged W-bosons (along with their wino superpartners). I determine a duality to a double Coulomb gas of neutral and magnetic bions of different charges of their constituent monopole-instantons, and W-bosons of both scalar and electric charges. Aharanov-Bohm interactions exist between magnetic bions and W-bosons, and scalar charges of W-bosons and neutral bions attract like charges, as opposed to the magnetic and electric charges where like charges repel. It is hoped in the future that lattice studies of this Coulomb gas can be done as in [1] for all gauge groups. It is hoped that a dual lattice 'affine' XY model with symmetry breaking perturbations can also be found in future studies of general gauge group as done in [1] for $SU(2)$.

Highlights

  • The difference from non-SUSY theories here is that the Higgsing along the thermal cycle gives rise to a light modulus scalar field which couples to both bion-instantons and the W-bosons, and mediates a transition near Tc where the bions and W-bosons compete with equal strengths

  • Aharanov-Bohm interactions exist between magnetic bions and W-bosons, and scalar charges of W-bosons and neutral bions attract like charges, as opposed to the magnetic and electric charges where like charges repel

  • ‘Resurgence’ theory has its role here. It is these neutral bions that allow for the centrestabilization of the gauge group in the vacuum of the theory, allowing for the confined phase where centre-symmetry is preserved at low temperatures, even though perturbative effective potentials tend to destabilize centre-symmetry

Read more

Summary

Outline and summary

In [1] the perturbative and non-perturbative contributions to the effective potential were calculated and dualities to a ‘double’ Coulomb gas of magnetic and neutral bions, as well as W bosons and their wino superpartners, was derived This was used in lattice studies along with a dual ‘affine’ XY-model with symmetry breaking perturbations coupled to a scalar field φ. The paper proceeds as follows: in section 2 I review the perturbative dynamics of Yang-Mills theory on R2 × SL1 × Sβ1 and its N = 1 supersymmetric version, beginning with the zero temperature case of R3 × SL1 in section 2.1 where I set up a notation valid for all gauge groups G.

F MN FMN
Monopole-instantons and bion structure at finite temperature
Duality to dual double Coulomb gas
Conclusions and future work
A Notes on Lie groups and Lie algebras
The roots and the weights
GPY effective potential derivation
Dual ‘double’ Coulomb gas derivation details
C Monopole solutions for all simple groups
Monopole solutions for arbitrary gauge group G
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call