Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNon-Renormalisation Theorems in Global Supersymmetry
67
0
0.0
(
0
)
Authors
J. Iliopoulos
Ask ChatGPT about the research
No Arabic abstract
We review the history of non-renormalisation theorems in global supersymmetry, as well as their importance in all attempts to apply supersymmetry to the real world.
rate research
Read More
The Zamolodchikov c-theorem has led to important new insights in our understanding of the renormalisation group and the geometry of the space of QFTs. Here, we review the parallel developments of the search for a higher-dimensional generalisation of the c-theorem and of the Local Renormalisation Group. The idea of renormalisation with position-dependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the local renormalisation group. The key role of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the c-theorem and four-dimensional a-theorem, is explained in detail. A number of different derivations of the c-theorem in two dimensions are presented -- using spectral functions, RG analysis of Green functions of the energy-momentum tensor T_{mu nu}, and dispersion relations -- and are generalised to four dimensions. The obstruction to establishing monotonic C-functions related to the beta_c and beta_b trace anomaly coefficients in four dimensions is discussed. The possibility of deriving an a-theorem, involving the coefficient beta_a of the Euler-Gauss-Bonnet density in the trace anomaly, is explored initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak a-theorem using a dispersion relation for four-point functions of T^mu_mu is presented. Finally, we describe the application of the local renormalisation group to the issue of limit cycles in theories with a global symmetry and it is shown how this sheds new light on the geometry of the space of couplings in QFT.
Non-minimal renormalisation schemes such as the momentum subtraction scheme (MOM) have frequently been used for physical computations. The consistency of such a scheme relies on the existence of a coupling redefinition linking it to MSbar. We discuss the implementation of this procedure in detail for a general theory and show how to construct the relevant redefinition up to three-loop order, for the case of a general theory of fermions and scalars in four dimensions and a general scalar theory in six dimensions.
This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D^2k R^4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide powerful constraints on the effective interactions. In the ten-dimensional IIA limit we find that there can be no perturbative contributions beyond k string loops (for k>0). Furthermore, the genus h=k contributions are determined exactly by the one-loop eleven-dimensional supergravity amplitude for all values of k. A plausible interpretation of these observations is that the sum of h-loop Feynman diagrams of maximally extended supergravity is less divergent than might be expected and could be ultraviolet finite in dimensions d < 4 + 6/h -- the same bound as for N=4 Yang--Mills.
We study non-topological, charged planar walls (Q-walls) in the context of a particle physics model with supersymmetry broken by low-energy gauge mediation. Analytical properties are derived within the flat-potential approximation for the flat-direction raising potential, while a numerical study is performed using the full two-loop supersymmetric potential. We analyze the energetics of finite-size Q-walls and compare them to Q-balls, non-topological solitons possessing spherical symmetry and arising in the same supersymmetric model. This allow us to draw a phase diagram in the charge-transverse length plane, which shows a region where Q-wall solutions are more stable than Q-balls.
We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
