# (Zoo of) Phase transitions in SUSY gauge theories

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In statistical physics and solid state physics at zero temperature ($T=0$), there are various quantum phase transitions that can be 1st order phase transitions or continuous (2nd order) phase transitions. One way to distinguish the two is to look at [the free energy and to see the critical exponents](https://en.wikipedia.org/wiki/Phase_transition). ;

1. What are some examples of phase transitions in Supersymmetry (SUSY) gauge theories at zero temperature ($T=0$)? Are there both continuous (2nd order) phase transitions, and 1st order phase transitions?

2. What are some examples of phase transitions in Supersymmetry (SUSY) gauge theories at finite temperature ($T>0$)? Are there both continuous (2nd order) phase transitions, and 1st order phase transitions?

Note:

(i) Here let us consider phase transitions in a more physical ground, based on tuning the relevant operator deformations (additional terms in the Lagrangian, e.g. $q L_{\text{deform}}$) at the UV high energy, and see what it flows to at IR.

(ii) Other types of physical tuning parameters are chemical potential $\mu$ (zero $T$) and temperature $T$ (to finite $T$), the $\mu$-$T$ are meaningful in the sense of QCD phase diagram.

(iii) If one had considered the physical relevant operator deformations (i) and (ii), then one can consider other non-physical tuning parameters, such as the number of color $N_c$, flavor $N_f$, etc. These types of parameters are much meaningless in the experiments.

One can often tune the vev of scalar fields in a susy gauge theory. In $\mathcal{N}=2$ SYM one  can tune the VEV of the scalars in adjoint of $SU(N)$ gauge group, so that the gauge group $SU(N)$ is "broken" (or rather "Higgsed" ) to various different extent (see section 3 of this note), and these phases have different number of massless and massive particles. Since this involves the appearance/disappearance of massless particles, I'd call the phase transitions 2nd order.
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