Higher Derivative Operators Research Articles

Interaction of anomaly-induced gravity with quantized matter and temperature effects

Matter fields during the very early Universe are described by GUT models in curved spacetime. At high energies these fields are asymptotically free and conformally coupled to the external metric. The only possible quantum effect is the appearance of the conformal anomaly, which leads to the propagation of the new degree of freedom, the conformal factor. Simultaneously with the expansion of the Universe, the scale of energies decreases and the propagating conformal factor starts to interact with the Higgs field due to the violation of conformal invariance in the matter fields sector. In a previous paper we have shown that this interaction can lead to special physical effects like renormalization group flow, which ends at some fixed point. Furthermore, in the vicinity of this fixed point the first-order phase transition may occur. In the present paper we consider the same theory of the conformal factor coupled to the Higgs field and incorporate the temperature effects. We reduce the complicated higher-derivative operator to several of standard second-derivative form and calculate an exact effective potential with temperature on the anti-de Sitter (AdS) background. The physical analysis of the effective potential is performed within the framework of the high-temperature expansion.

Higher derivative terms in the effective action of N = 2 SUSY QCD from instantons

We consider N = 2 SUSY QCD with gauge group SU(2) and N f flavours of matter with non-zero mass. Using the method of the instanton-induced effective vertex we calculate higher derivative corrections to the Seiberg-Witten result in the momuntum expansion of the low energy effective Lagrangian in various regions of the modular space. Then we focus on a certain higher derivative operator on the Higgs branch. We show that the singular behaviour of this operator comes from values of the mass of matter at which the charge singularity on the Coulomb branch collides with the monopole or dyon singularity. Given the behaviour of this operator at weak coupling coming from instantons as well as its behaviour near the points of colliding singularities we find the exact solution for this operator.

Comments on higher derivative operators in some SUSY field theories

We study the leading irrelevant operators along the flat directions of certain supersymmetric theories. In particular, we focus on finite N = 2 (including N = 4) supersymmetric field theories in four dimensions and show that these operators are completely determined by the symmetries of the problem. This shows that they are generated only at one loop and are not renormalized beyond this order. An instanton computation in similar three dimensional theories shows that these terms are renormalized. Hence, the four dimensional non-renormalization theorem of these terms is not valid in three dimensions.

A correction to the Hamiltonian of the QCD string with quarks due to the rigidity term

A correction to the Hamiltonian of the quark-antiquark system, arising due to the rigidity term in the gluodynamics string effective action, is obtained. This correction contains additional contributions to the orbital momentum of the system and several higher derivative operators. With the help of the derived Hamiltonian a rigid string-induced term in the Hamiltonian of the relativistic quark model is evaluated for the case of large masses of a quark and antiquark.

Strongly interacting Higgs sector without technicolor

Several years ago, we proposed a modification of the Standard Model, in which the Higgs sector was stabilized by the addition of higher derivative operators, similar to Lee-Wick Electrodynamics. We studied this theory extensively, both using continuum Hamiltonian and path integral methods. We also reported detailed lattice studies of the higher derivative Higgs sector. In view of some recent revived interest in our original idea, we are providing here our extensive notes from the time period on this topic. The key results were already published in our papers at that time. The many additional details that we make available here were previously available only in Chuan Liu's UCSD Ph.D. thesis (1994). Very recently, our idea has been revived by other groups. In view of the renewed interest, and to perhaps correct some misconceptions in the literature, we are here making our original extensive notes available to the wider community.

Higher-derivative operators and DeWitt's WKB ansatz.

We investigate the short-distance behaviors of the higher-derivative operators appearing in some field theories which attracted much interest recently, for instance, higher-derivative quantum gravity. This study is important to find the short-distance structures of the related propagators and the one-loop divergences. We develop an algorithm which can be used to find asymptotic expansions of the heat kernels for higher-derivative operators. Our method is applicable both to flat-- and to curved--space-time cases.