8,368 research outputs found

### Renormalisation of the Fayet-Iliopoulos D-term

We consider the renormalisation of the Fayet-Iliopoulos D-term in a
softly-broken Abelian supersymmetric theory. We show that there exists (at
least through three loops) a renormalisation group invariant trajectory for the
coefficient of the D-term, corresponding to the conformal anomaly solution for
the soft masses and couplings.Comment: 11 pages, TeX, Uses Harvmac (big). References added, minor
corrections (including a sign error for the zeta(3) terms), and discussion of
scheme dependence corrected and amplifie

### The Full Two-Loop R-parity Violating Renormalization Group Equations for All Minimal Supersymmetric Standard Model Couplings

We present the full two-loop $\beta$-functions for the minimal supersymmetric
standard model couplings, extended to include R-parity violating couplings
through explicit R-parity violation

### A three-loop check of the 'a - maximization' in SQCD with adjoint(s)

The 'a - maximization' was introduced by K. Inrtiligator and B. Wecht for
finding anomalous dimensions of chiral superfields at the IR fixed points of
the RG flow. Using known explicit calculations of anomalous dimensions in the
perturbation theory of SQCD (with one or two additional adjoint fields), it is
checked here at the three-loop level.Comment: 5 pages; the title changed, the text improved and expande

### The Fayet-Iliopoulos D-term and its renormalisation in softly-broken supersymmetric theories

We consider the renormalisation of the Fayet-Iliopoulos D-term in a
softly-broken abelian supersymmetric theory, and calculate the associated
beta-function through three loops. We show that there exists (at least through
three loops) a renormalisation group invariant trajectory for the coefficient
of the D-term, corresponding to the conformal anomaly solution for the soft
masses and couplings.Comment: 30 pages, Revtex, 15 Figures. Minor changes, and inadvertent omission
of author from this abstract correcte

### The Fayet-Iliopoulos D-term and its renormalisation in the MSSM

We consider the renormalisation of the Fayet-Iliopoulos D-term in a
softly-broken supersymmetric gauge theory with a non-simple gauge group
containing an abelian factor, and present the associated beta-function through
three loops. We also include in an appendix the result for several abelian
factors. We specialise to the case of the minimal supersymmetric standard model
(MSSM), and investigate the behaviour of the Fayet-Iliopoulos coupling for
various boundary conditions at the unification scale. We focus particularly on
the case of non-standard soft supersymmetry breaking couplings, for which the
Fayet-Iliopoulos coupling evolves significantly between the unification scale
and the weak scale.Comment: 18 pages, Revtex, 2 figures. Expanded version including general
results for gauge groups with several abelian factors. Minor typos correcte

### Constraints on RG Flow for Four Dimensional Quantum Field Theories

The response of four dimensional quantum field theories to a Weyl rescaling
of the metric in the presence of local couplings and which involve $a$, the
coefficient of the Euler density in the energy momentum tensor trace on curved
space, is reconsidered. Previous consistency conditions for the anomalous
terms, which implicitly define a metric $G$ on the space of couplings and give
rise to gradient flow like equations for $a$, are derived taking into account
the role of lower dimension operators. The results for infinitesimal Weyl
rescaling are integrated to finite rescalings $e^{2\sigma}$ to a form which
involves running couplings $g_\sigma$ and which interpolates between IR and UV
fixed points. The results are also restricted to flat space where they give
rise to broken conformal Ward identities. Expressions for the three loop Yukawa
$\beta$-functions for a general scalar/fermion theory are obtained and the
three loop contribution to the metric $G$ for this theory are also calculated.
These results are used to check the gradient flow equations to higher order
than previously. It is shown that these are only valid when $\beta \to B$, a
modified $\beta$-function, and that the equations provide strong constraints on
the detailed form of the three loop Yukawa $\beta$-function. ${\cal N}=1$
supersymmetric Wess-Zumino theories are also considered as a special case. It
is shown that the metric for the complex couplings in such theories may be
restricted to a hermitian form.Comment: 86 pages, version 2, various corrections, section 3 significantly
revised, version 3 further minor corrections, as to be published, version 4,
some corrections and additional material in sections 2,

### WZW-Toda Reduction using the Casimir Operator

We construct a quantum Hamiltonian operator for the Wess-Zumino-Witten (WZW)
model in terms of the Casimir operator. This facilitates the discussion of the
reduction of the WZW model to Toda field theory at the quantum level and
provides a very straightforward derivation of the quantum central charge for
the Toda field theory.Comment: 16pp, uses harvmac, LTH 304 (Revised version with improved discussion
of non-perturbative effects

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