Asymptotic Padé Approximants and the SQCD $β$-function
We present a prediction for the four loop $β$-function for SQCD based on the method of Asymptotic Padé Approximants.
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arXiv subjects
D. R. T. Jones
Publications and source records attributed to D. R. T. Jones.
$β$-functions in large-$N_f$ supersymmetric gauge theories
We present calculations of the leading and $O(1/N_f)$ terms in a large-$N_f$ expansion of the $β$-functions and anomalous dimensions for various supersymmetric gauge theories, including supersymmetric QCD. In the case of supersymmetric QCD, we show that our $O(1/N_f)$ approximation displays an infra-red fixed point in the conformal window $3N_c/2 < N_f < 3N_c$.
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Large-N supersymmetric beta-functions
We present calculations of the leading and O(1/N) terms in a large-N expansion of the β-functions for various supersymmetric theories: a Wess-Zumino model, supersymmetric QED and a non-abelian supersymmetric gauge theory. In all cases N is the number of a class of the chiral superfields in the theory.
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The three-loop SSM $β$-functions
We present the supersymmetric standard model three-loop $β$-functions for gauge and Yukawa couplings and consider the effect of three-loop corrections on the standard running coupling analyses.
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Scheme dependence and the NSVZ $β$-function
We investigate the connection between the NSVZ and the DRED forms of the gauge $β$-function in an $N=1$ supersymmetric gauge theory. We construct a coupling constant redefinition that relates the two forms up to four loops. By abelian calculations, we are able to infer the complete non-abelian form of $β_g^{(3)DRED}$, and also $β_g^{(4)DRED}$ except for one undetermined parameter.
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$N=1$ supersymmetry and the three loop gauge beta function
We calculate the three loop gauge $β$-function for an abelian $N=1$ supersymmetric gauge theory, using DRED. We construct a coupling constant redefinition that relates the result to the corresponding term in the NSVZ $β$-function, and by generalising this redefinition to the non-abelian case we derive the DRED three loop gauge $β$-function for the non-abelian case.
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$N=1$ supersymmetry and the three loop anomalous dimension for the chiral superfield
We calculate the three loop anomalous dimension for a general $N=1$ supersymmetric gauge theory. The result is used to probe the possible existence of renormalisation invariant relationships between the Yukawa and gauge couplings.
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Infra--red soft universality
We show that in a special class of theories the commonly assumed universal form of the soft supersymmetry--breaking terms is approached in the infra--red limit. The resulting universal scalar mass and trilinear coupling are predicted in terms of the gaugino mass.
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Universality and the sparticle spectrum
We calculate the particle spectrum of the SSM which follows from the assumption that the commonly assumed universal form of the soft supersymmetry --breaking terms is invariant under renormalisation. It is argued that this ``strong'' universality might be approached as an infra--red fixed point for the unified theory above the unification scale.
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Renormalisation-group invariance and soft supersymmetry-breaking
We show that a particular ``universal'' form for the soft-breaking couplings in a softly broken $N=1$ supersymmetric gauge theory is renormalisation-group invariant through two loops, provided we impose one simple condition on the dimensionless couplings. The universal form for the trilinear couplings and mass terms is identical to that found in popular derivations of the soft-breaking terms from strings or supergravity.
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Soft supersymmetry breaking and finiteness
We calculate the two-loop $β$-functions for soft supersymmetry-breaking interactions in a general supersymmetric gauge theory, emphasising the role of the evanescent couplings and masses that are generic to a non-supersymmetric theory. We also show that a simple set of conditions sufficient for one-loop finiteness renders a theory two-loop finite, and we speculate on the possible significance of finite softly broken theories.
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Equivalence of Dimensional Reduction and Dimensional Regularisation
For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional regularisation (DREG), to all orders in perturbation theory and for a general renormalisable theory. The two regularisation schemes are related by an analytic redefinition of the couplings, under which the $\b$-functions calculated using DRED transform into those computed in DREG. The $S$-matrix calculated using DRED is numerically equal to the DREG version, ensuring that both schemes give the same physics.
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Six-loop divergences in the supersymmetric Kahler sigma model
The two-dimensional supersymmetric $\s$-model on a Kähler manifold has a non-vanishing $\b$-function at four loops, but the $\b$-function at five loops can be made to vanish by a specific choice of renormalisation scheme. We investigate whether this phenomenon persists at six loops, and conclude that it does not; there is a non-vanishing six-loop $\b$-function irrespective of renormalisation scheme ambiguities.
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Dimensional Reduction in Non-Supersymmetric Theories
It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.
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The Exact Tachyon Beta-Function for the Wess-Zumino-Witten Model
We derive an exact expression for the tachyon $β$-function for the Wess-Zumino-Witten model. We check our result up to three loops by calculating the three-loop tachyon $β$-function for a general non-linear $σ$-model with torsion, and then specialising to the case of the WZW model.
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Quantum Non-abelian Toda Field Theories
We derive an explicit, exactly conformally invariant form for the action for the non-abelian Toda field theory. We demonstrate that the conformal invariance conditions, expressed in terms of the $β$-functions of the theory, are satisfied to all orders, and we use our results to obtain a value for the central charge agreeing with previous calculations.
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The effective potential and the renormalisation group
We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.
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Exact Bosonic and Supersymmetric String Black Hole Solutions
We show that Witten's two-dimensional string black hole metric is exactly conformally invariant in the supersymmetric case. We also demonstrate that this metric, together with a recently proposed exact metric for the bosonic case, are respectively consistent with the supersymmetric and bosonic $σ$-model conformal invariance conditions up to four-loop order.
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