Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe 2PI effective action at four loop order in $varphi^4$ theory
97
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
It is well known that perturbative pressure calculations show poor convergence. Calculations using a two particle irreducible (2PI) effective action show improved convergence at the 3 loop level, but no calculations have been done at 4 loops. We consider the 2PI effective theory for a symmetric scalar theory with quartic coupling in 4-dimensions. We calculate the pressure and two different non-perturbative vertices as functions of coupling and temperature. Our results show that the 4 loop contribution can become larger than the 3 loop term when the coupling is large. This indicates a breakdown of the 2PI approach, and the need for higher order $n$PI approximations. In addition, our results demonstrate the renormalizability of 2PI calculations at the 4 loop level. This is interesting because the counterterm structure of the 2PI theory at 4 loops is different from the structure at $nle 3$ loops. Two vertex counterterms are required at the 4 loop level, but not at lower loop order. This unique feature of the 2PI theory has not previously been verified numerically.
rate research
Read More
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.
We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N=4 Konishi supermultiplet.
We study the gauge transformation of the recently computed one-loop four-point function of {cal N}=4 supersymmetric Yang-Mills theory with gauge group U(N). The contributions from nonplanar diagrams are not gauge invariant. We compute their gauge variation and show that it is cancelled by the variation from corresponding terms of the one-loop five-point function. This mechanism is general: it insures the gauge invariance of the noncommutative one-loop effective action.
We compute the dilatation generator in the su(2) sector of planar N=4 super Yang-Mills theory at four-loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed directly from Feynman diagrams. This allows us to confirm previous conjectures for the leading contribution to the dressing phase which is proportional to zeta(3).
We consider the one-loop five-graviton amplitude in type II string theory calculated in the light-cone gauge. Although it is not possible to explicitly evaluate the integrals over the positions of the vertex operators, a low-energy expansion can be obtained, which can then be used to infer terms in the low-energy effective action. After subtracting diagrams due to known D^{2n}R^4 terms, we show the absence of one-loop R^5 and D^2R^5 terms and determine the exact structure of the one-loop D^4R^5 terms where, interestingly, the coefficient in front of the D^4R^5 terms is identical to the coefficient in front of the D^6R^4 term. Finally, we show that, up to D^6R^4 ~ D^4R^5, the epsilon_{10} terms package together with the t_8 terms in the usual combination (t_8t_8pm{1/8}epsilon_{10}epsilon_{10}).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
