The project is to find the spacial string tension for same N_t=8,10,12 where as N_s or N_sigma is >=4 N_t, where as the lattice spacing is set from sommer parameter, (r_0=.469 fm).
We are going to calculate this between temperature range 150 MeV to 500 MeV. Previously some calculation of spacial string tension has been done by M.Cheng et al in temperature range(0.9Tc to 4Tc).Due to this temperature range and number of temporal lattice sizes; the lattice size varied from 0.3fm to 0.05fm.

The two major differences are;  we are going to use HISQ action as opposed to p4fat3 (which adds bended 3 link term to standard staggered action and 1 link gauge connections are smeared with 3 link staples) staggered action for fermions and wilson plaquette with ractanguler term for gauge fields, and we are calculating with N_t=8,10,12. They found the result of spatial string tension from spatial qq* potential, which they calculated in background of (2light +1 heavy) flavour QCD. The masses of heavy quark corresponds to that of physical strange quark mass(M_s), and masses of light quarks corresponds to that of almost physical up and down quarks (m=0.1 M_s){which corresponds to pion mass of 220 MeV}. They found that the comparision that they made with diamensional reduction technique only holds upto temperature 1.5 Tc (Tc=160Mev Click to read more

However their study was limited by use of p4fat3 action and more importantly by the use of smeared wilson loops as the smeared wilson loops at numerically accessible perimeters are not well suited for studying string breaking, so they could not find any string breaking at high temperature spatial potentials. We can use polyakov loop correlation functions which are more sensitive to string breaking effects in spatial potentials. They found that the spatial potential was increasing linearly with the temperature, we would like to check that with HISQ action with different N_t set(8,10,12 as opposed to 4,6,8).

One reason we would like to check it becuase the calcuation has been done in 2 flavour QCD using wilson fermions with significantly large quark masses and we found no temperature dependence. It remains to be seen to what extent these discrepancies are present in wilson fermions (due to larger quark masses in SU(2) or cut off effects or limited statistics), but one hesitates as the wilson fermions are numerically more demanding.

There will be uncertainities when we compare data on spatial string tension :

1. Scale dependence of the 3d gauge coupling.
2. The uncertainity in value of coefficient 'c'.
3. Uncertainity in value of r_0* (lambda_minimal substration) They reduced the uncertainities in last two source by caculating lattice beta function for the p4fat3 action perturbatively and through a more precise calculation of the string tension on 3d adjoint higgs model.

They calculated the spatial wilson loops on gauge configurations (they generated 30,000 gauge configurations at each temperature by RHMC algorithm) which were seperated by 10 RHMC (Relational Hybrid Monte Carlo) trajectories. To reduce autocorrelation the measurements were bunched into blocks and errors on aV_s(R) was calculated using Jackknife samples. They also varied the block-size of Jackknife samples and found that errors don't change significantly.