Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups

We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our theories have only gauge fields and fermions, and we compute the UV divergent part of the one-loop background-field effective action involving two fermionic fields at first order in the noncommutativity parameter theta. We show that, if the second-degree Casimir has the same value for all the irreps furnished by the fermionic multiplets of the model, then, that UV divergent part can be renormalised by carrying out multiplicative renormalisations of the coupling constant, theta and the fields, along with the inclusion of theta-dependent counterterms which vanish upon imposing the equations of motion. These theta-dependent counterterms have no physical effect since they vanish on-shell. This result along with the vanishing of the UV divergent part of the fermionic four-point functions leads to the unexpected conclusion that the one-loop matter sector of the background-field effective action of these theories is one-loop multiplicatively renormalisable on-shell. We also show that the background-field effective action of the gauge sector of the theories considered here receives no theta-dependent UV divergent contributions at one-loop. We thus conclude that these theories are on-shell one-loop multiplicatively renormalisable at first order in theta.Comment: 20 pages, 3 figure

Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix \theta^{\mu\nu} the UV divergent part of its effective action in the background-field gauge, and, for N>=2, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain --for N>=3, the case with N=2 being trivial-- the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.Comment: 33 pages, 4 figures. Version 2: Unnecessary files removed. Version 3: New types of field redefinitions were considered, which make the large N U(N) and the SU(N) theories renormalisable. The conclusions for U(N) with finite N remain unchanged. Version 4: Corrected mistyped equations, minor revision

Shift versus no-shift in local regularizations of Chern-Simons theory

We consider a family of local BRS-invariant higher covariant derivative regularizations of $SU(N)$ Chern-Simons theory that do not shift the value of the Chern-Simons parameter $k$ to k+\,{\rm sign}(k)\,\cv at one loop.Comment: phyzzx, 6 pages, FTUAM 94/8, NIKHEF-H 94/14 and UPRF 93/39

Decoupling in an expanding universe: boundary RG-flow affects initial conditions for inflation

We study decoupling in FRW spacetimes, emphasizing a Lagrangian description throughout. To account for the vacuum choice ambiguity in cosmological settings, we introduce an arbitrary boundary action representing the initial conditions. RG flow in these spacetimes naturally affects the boundary interactions. As a consequence the boundary conditions are sensitive to high-energy physics through irrelevant terms in the boundary action. Using scalar field theory as an example, we derive the leading dimension four irrelevant boundary operators. We discuss how the known vacuum choices, e.g. the Bunch-Davies vacuum, appear in the Lagrangian description and square with decoupling. For all choices of boundary conditions encoded by relevant boundary operators, of which the known ones are a subset, backreaction is under control. All, moreover, will generically feel the influence of high-energy physics through irrelevant (dimension four) boundary corrections. Having established a coherent effective field theory framework including the vacuum choice ambiguity, we derive an explicit expression for the power spectrum of inflationary density perturbations including the leading high energy corrections. In accordance with the dimensionality of the leading irrelevant operators, the effect of high energy physics is linearly proportional to the Hubble radius H and the scale of new physics L= 1/M.Comment: LaTeX plus axodraw figures. v2: minor corrections; refs added. JHEP style: 34 pages + 18 pages appendi

Interacting Dipoles from Matrix Formulation of Noncommutative Gauge Theories

We study the IR behavior of noncommutative gauge theory in the matrix formulation. We find that in this approach, the nature of the UV/IR mixing is easily understood, which allows us to perform a reliable calculation of the quantum effective action for the long wavelength modes of the noncommutative gauge field. At one loop, we find that our description is weakly coupled only in the supersymmetric theory. At two loops, we find non-trivial interaction terms suggestive of dipole degrees of freedom. These dipoles exhibit a channel duality reminiscent of string theory.Comment: LaTeX 11 pages, 4 figures; v.2 minor changes and some references added; v.3 many more technical details added and significantly different presentation, use REVTeX 4, to appear in PR

The Effective Potential, the Renormalisation Group and Vacuum Stability

We review the calculation of the the effective potential with particular emphasis on cases when the tree potential or the renormalisation-group-improved, radiatively corrected potential exhibits non-convex behaviour. We illustrate this in a simple Yukawa model which exhibits a novel kind of dimensional transmutation. We also review briefly earlier work on the Standard Model. We conclude that, despite some recent claims to the contrary, it can be possible to infer reliably that the tree vacuum does not represent the true ground state of the theory.Comment: 23 pages; 5 figures; v2 includes minor changes in text and additional reference

The universality of the shift of the Chern-Simons parameter for a general class of BRS invariant regularizations

We consider a biparametric family of BRS invariant regularization methods of SU(N) Chern-Simons theory (the parameters defining the family taking arbitrary values in \RR^2) and show that the shift $k\to k + sign(k) N$ of the Chern-Simons parameter $k$ occurs for arbitrary values of the family defining parameters. This supports irrefutably the conjecture that the shift of $k$ is universal for BRS invariant regulators.Comment: phyzzx, 7 pages (no figures

Fibre Inflation: Observable Gravity Waves from IIB String Compactifications

We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential $V = V_0 (3-4 e^{-\hat\varphi/\sqrt{3}})$. Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient $V_0$, and in particular do not enter into the slow-roll parameters. Consequently these are determined purely by the number of \e-foldings, $N_e$, and so are not independent: $\varepsilon \simeq \frac32 \eta^2$. This implies similar relations among observables like the primordial scalar-to-tensor amplitude, $r$, and the scalar spectral tilt, $n_s$: $r \simeq 6(n_s - 1)^2$. $N_e$ is itself more model-dependent since it depends partly on the post-inflationary reheat history. In a simple reheating scenario a reheating temperature of $T_{rh}\simeq 10^{9}$ GeV gives $N_e\simeq 58$, corresponding to $n_s\simeq 0.970$ and $r\simeq 0.005$, within reach of future observations. The model is an example of a class that arises naturally in the context of type IIB string compactifications with large-volume moduli stabilisation, and takes advantage of the generic existence there of Kahler moduli whose dominant appearance in the scalar potential arises from string loop corrections to the Kahler potential. The inflaton field is a combination of Kahler moduli of a K3-fibered Calabi-Yau manifold. We believe there are likely to be a great number of models in this class -- `high-fibre models' -- in which the inflaton starts off far enough up the fibre to produce observably large primordial gravity waves.Comment: Extended calculations beyond the leading approximations, including numerical integrations of multi-field evolution; Display an example with $r = 0.01$; Simplify the discussion of large fields; Corrected minor errors and typos; Added references; 41 pages LaTeX, 25 figure

Glueballs, symmetry breaking and axionic strings in non-supersymmetric deformations of the Klebanov-Strassler background

We obtain an analytic solution for an axionic non-supersymmetric deformation of the warped deformed conifold. This allows us to study D-strings in the infrared limit of non-supersymmetric deformations of the Klebanov-Strassler background. They are interpreted as axionic strings in the dual field theory. Following the arguments of [hep-th/0405282], the axion is a massless pseudo-scalar glueball which is present in the supergravity fluctuation spectrum and it is interpreted as the Goldstone boson of the spontaneously broken U(1) baryon number symmetry, being the gauge theory on the baryonic branch. Besides, we briefly discuss about the Pando Zayas-Tseytlin solution where the SU(2) \times SU(2) global symmetry is spontaneously broken. This background has been conjectured to be on the mesonic branch of the gauge theory.Comment: 30 pages; V2: minor corrections; V3: section 3 corrected and misprints corrected to match version published in JHE