Related papers: Direct Monte Carlo Computation of the 't~Hooft Par…
We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the K\"ahler form with jumps…
For quantum field theories with global symmetry, we can study the behavior of the partition function with the background gauge field to diagnose different quantum phases. For the case of discrete symmetries, we find that the…
The partition function of a massless scalar field on a Euclidean spacetime manifold $\mathbb{R}^{d-1}\times\mathbb{T}^2$ and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is…
We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle…
Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function…
We give a direct path-integral calculation of the partition function for pure 3+1 dimensional U(N) Yang-Mills theory at large N on a small three-sphere, up to two-loop order in perturbation theory. From this, we calculate the one-loop shift…
For an even integer t \geq 2, the Matchings Connecivity matrix H_t is a matrix that has rows and columns both labeled by all perfect matchings of the complete graph K_t on t vertices; an entry H_t[M_1,M_2] is 1 if M_1\cup M_2 is a…
A relation between circular 1/2 BPS 't Hooft operators in 4d N=4 SYM and instantonic solutions in 2d Yang-Mills theory (YM_2) has recently been conjectured. Localization indeed predicts that those 't Hooft operators in a theory with gauge…
We revisit the localization computation of the expectation values of 't Hooft operators in $\mathcal{N}=2^*$ SU(N) theory on $\mathbb{R}^3 \times S^1$. We show that the part of the answer arising from "monopole bubbling" on $\mathbb{R}^3$…
We derive exact formulae for the partition function and the expectation values of Wilson/'t Hooft loops, thus directly checking their S-duality transformations. We focus on a special class of N=2 gauge theories on S^4 with fundamental…
The partition function of four dimensional SO(4) Yang-Mills theory is rewritten in terms of variables admitting straightforward relation to the partition function of pure 4D gravity. The gauge action turns into first-order Hilbert-Palatini…
The spatial 't Hooft loop measures the colour electric flux in SU(N)/Z(N) gauge theory. It is a closed loop of Dirac Z(N) flux and has strength k=1, 2,.., N-1. It is analyzed for generic k and small gauge coupling in the high temperature…
Topologically twisted $\mathcal{N} = 4$ super Yang-Mills theory has a partition function that counts Euler numbers of instanton moduli spaces. On the manifold $\mathbb{P}^2$ and with gauge group $\mathrm{U}(3)$ this partition function has a…
We use 't Hooft loops of maximal size on finite lattices to calculate the free energy in the sectors of SU(2) Yang-Mills theory with fixed electric flux as a function of temperature and (spatial) volume. Our results provide evidence for the…
We provide a quantum path integral definition of an 't Hooft loop operator, which inserts a pointlike monopole in a four dimensional gauge theory. We explicitly compute the expectation value of the circular 't Hooft operators in N=4 super…
We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional $\mathcal{N} =4$ super Yang-Mills theory on $\mathbb{CP}^{2}$ for the gauge group $SO(3)$ from the path integral of the effective…
Efficient and accurate algorithm for partition function, free energy and thermal entropy calculations is of great significance in statistical physics and quantum many-body physics. Here we present an unbiased but low-technical-barrier…
The effective action in gauge theories is known to depend on a choice of gauge fixing conditions. This dependence is such that any change of gauge conditions is equivalent to a field redefinition in the effective action. In this sense, the…
We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric K\"ahler manifolds, with particular emphasis on $\mathbb{CP}^2$. By choosing a vector generating a $U(1)$ action inside the torus of the manifold, we construct…
We derive the partition function of {\cal N}=4 supersymmetric Yang-Mills theory on orbifold-T^4/{\bf Z}_2 for gauge group SU(N). We generalize the method of our previous work for the SU(2) case to the SU(N) case. The resulting partition…