Gauge Coupling Function Research Articles

6d mathcal{N} = (1, 0) anomalies on S1 and F-theory implications

We show that the pure gauge anomalies of 6d mathcal{N} = (1, 0) theories compactified on a circle are captured by field-dependent Chern-Simons terms appearing at one-loop in the 5d effective theories. These terms vanish if and only if anomalies are canceled. In order to obtain this result, it is crucial to integrate out the massive Kaluza-Klein modes in a way that preserves 6d Lorentz invariance; the often-used zeta-function regularization is not sufficient. Since such field-dependent Chern-Simons terms do not arise in the reduction of M-theory on a threefold, six-dimensional F-theory compactifications are automatically anomaly free, whenever the M/F-duality can be used. A perfect match is then found between the 5d mathcal{N} = 1 prepotentials of the classical M-theory reduction and one-loop circle compactification of an anomaly free theory. Finally, from this potential, we read off the quantum corrections to the gauge coupling functions.

Shift-symmetries and gauge coupling functions in orientifolds and F-theory

We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We generalize this discussion to a genuine F-theory compactification on an elliptically fibered Calabi-Yau fourfold. We perform the first general dimensional reduction of eleven-dimensional super-gravity and dualization to the F-theory frame. The resulting effective action is compared with the circle reduction of a four-dimensional mathcal{N} = 1 supergravity theory. The F-theory geometry elegantly unifies bulk and brane degrees of freedom and allows us to infer non-trivial results about holomorphicity and shift-symmetries. For instance, we gain new insight into kinetic mixing of bulk and brane gauge fields.

Anisotropic inflation in Gauss-Bonnet gravity

We study anisotropic inflation with Gauss-Bonnet correction in presence of a massless vector field. In this scenario, exact anisotropic power-law inflation is realized when the inflaton potential, gauge coupling function and the Gauss-Bonnet coupling are exponential functions. We show that anisotropy becomes proportional to two slow-roll parameters of the theory and hence gets enhanced in presence of quadratic curvature corrections. The stability analysis reveals that anisotropic power-law solutions remain stable over a substantially large parameter region.

Non-Abelian discrete gauge symmetries in F-theory

The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.

Spatial modulation and conductivities in effective holographic theories

We analyze a class of bottom-up holographic models for low energy thermo-electric transport. The models we focus on belong to a family of Einstein-Maxwell-dilaton theories parameterized by two scalar functions, characterizing the dilaton self-interaction and the gauge coupling function. We impose spatially inhomogeneous lattice boundary conditions for the dilaton on the AdS boundary and study the resulting phase structure attained at low energies. We find that as we dial the scalar functions at our disposal (changing thus the theory under consideration), we obtain either (i) coherent metallic, or (ii) insulating, or (iii) incoherent metallic phases. We chart out the domain where the incoherent metals appear in a restricted parameter space of theories. We also analyze the optical conductivity, noting that non-trivial scaling behaviour at intermediate frequencies appears to only be possible for very narrow regions of parameter space.

Inflation in maximal gauged supergravities

We discuss the dynamics of multiple scalar fields and the possibility of realistic inflation in the maximal gauged supergravity. In this paper, we address this problem in the framework of recently discovered 1-parameter deformation of SO(4,4) and SO(5,3) dyonic gaugings, for which the base point of the scalar manifold corresponds to an unstable de Sitter critical point. In the gauge-field frame where the embedding tensor takes the value in the sum of the {\\bf 36} and {\\bf 36'} representations of SL(8), we present a scheme that allows us to derive an analytic expression for the scalar potential. With the help of this formalism, we derive the full potential and gauge coupling functions in analytic forms for the SO(3)× SO(3)-invariant subsectors of SO(4,4) and SO(5,3) gaugings, and argue that there exist no new critical points in addition to those discovered so far. For the SO(4,4) gauging, we also study the behavior of 6-dimensional scalar fields in this sector near the Dall'Agata-Inverso de Sitter critical point at which the negative eigenvalue of the scalar mass square with the largest modulus goes to zero as the deformation parameter s approaches a critical value sc. We find that when the deformation parameter s is taken sufficiently close to the critical value, inflation lasts more than 60 e-folds even if the initial point of the inflaton allows an O(0.1) deviation in Planck units from the Dall'Agata-Inverso critical point. It turns out that the spectral index ns of the curvature perturbation at the time of the 60 e-folding number is always about 0.96 and within the 1σ range ns=0.9639±0.0047 obtained by Planck, irrespective of the value of the η parameter at the critical saddle point. The tensor-scalar ratio predicted by this model is around 10−3 and is close to the value in the Starobinsky model.

Mass sum rule of the effective action on vacua with broken rigid [formula omitted] supersymmetry

We present an extension of the mass sum rule that applies to renormalizable rigid supersymmetric field theories to the case of the N=1 supersymmetric effective action (the gauged non-linear sigma model) consisting of adjoint scalar superfields and vector superfields possessing a Kähler potential, a set of gauge coupling functions (second prepotential derivatives) and a superpotential, which respectively set their energy scales. The mass sum rule derived is valid for any vacua, including the (metastable) one of broken supersymmetry with the condensates of D-term and/or F-term. We manage to extend these analyses to the cases where superfields in (anti-)fundamental representation are present. The supertrace is shown to vanish in those cases where underlying geometry is special Kähler and theory under concern is anomaly free. Simple phenomenological application is given, providing an upper bound for gaugino masses. We discuss that the effects of the D and/or F condensates can be represented as a set of soft breaking terms with their strengths predicted by the scales.

Fluxes and warping for gauge couplings in F-theory

We compute flux-dependent corrections in the four-dimensional F-theory effective action using the M-theory dual description. In M-theory the 7-brane fluxes are encoded by four-form flux and modify the background geometry and Kaluza-Klein reduction ansatz. In particular, the flux sources a warp factor which also depends on the torus directions of the compactification fourfold. This dependence is crucial in the derivation of the four-dimensional action, although the torus fiber is auxiliary in F-theory. In M-theory the 7-branes are described by an infinite array of Taub-NUT spaces. We use the explicit metric on this geometry to derive the locally corrected warp factor and M-theory three-from as closed expressions. We focus on contributions to the 7-brane gauge coupling function from this M-theory back-reaction and show that terms quadratic in the internal seven-brane flux are induced. The real part of the gauge coupling function is modified by the M-theory warp factor while the imaginary part is corrected due to a modified M-theory three-form potential. The obtained contributions match the known weak string coupling result, but also yield additional terms suppressed at weak coupling. This shows that the completion of the M-theory reduction opens the way to compute various corrections in a genuine F-theory setting away from the weak string coupling limit.

The [formula omitted] effective actions of D-branes in Type IIA and IIB orientifolds

We discuss the four-dimensional N = 1 effective actions of single space–time filling D p -branes in general Type IIA and Type IIB Calabi–Yau orientifold compactifications. The effective actions depend on an infinite number of normal deformations and gauge connection modes. For D6-branes the N = 1 Kähler potential, the gauge-coupling function, the superpotential and the D-terms are determined as functions of these fields. They can be expressed as integrals over chains which end on the D-brane cycle and a reference cycle. The infinite deformation space will reduce to a finite dimensional moduli space of special Lagrangian submanifolds upon imposing F- and D-term supersymmetry conditions. We show that the Type IIA moduli space geometry is captured by three real functionals encoding the deformations of special Lagrangian submanifolds, holomorphic three-forms and Kähler two-forms of Calabi–Yau manifolds. These elegantly combine in the N = 1 Kähler potential, which reduces after applying mirror symmetry to the results previously determined for space–time filling D3-, D5- and D7-branes. We also propose general chain integral expressions for the Kähler potentials of Type IIB D-branes.

The [formula omitted] effective action of F-theory compactifications

The four-dimensional N=1 effective action of F-theory compactified on a Calabi–Yau fourfold is studied by lifting a three-dimensional M-theory compactification. The lift is performed by using T-duality realized via a Legendre transform on the level of the effective action, and the application of vector-scalar duality in three dimensions. The leading order Kähler potential and gauge-kinetic coupling functions are determined. In these compactifications two sources of gauge theories are present. Space–time filling non-Abelian seven-branes arise at the singularities of the elliptic fibration of the fourfold. Their couplings are included by resolving the singular fourfold. Generically a U(1)r gauge theory arises from the R–R bulk sector if the base of the elliptically fibered Calabi–Yau fourfold supports 2r harmonic three-forms. The gauge coupling functions depend holomorphically on the complex structure moduli of the fourfold, comprising closed and open string degrees of freedom. The four-dimensional electro-magnetic duality is studied in the three-dimensional effective theory obtained after M-theory compactification. A discussion of matter couplings transforming in the adjoint of the seven-brane gauge group is included.

Heterotic strings on generalized Calabi–Yau manifolds and Kaehler moduli stabilization

Compactifications of heterotic string theory on generalized Calabi–Yau manifolds with SU(3) structure, have been expected to give the same type of flexibility that type IIB compactifications on Calabi–Yau orientifolds have. In this note we generalize the work done on half-flat manifolds by other authors, to show how flux quantization occurs in the general case, by starting with a basis of harmonic forms and then extending it. However it turns out that only the axions associated with the non-harmonic directions in the space of Kaehler moduli, can be stabilized by the geometric (torsion) terms. Also we argue that there are no supersymmetric extrema of the potential when the second (and fourth) cohomology groups on the manifold are non-trivial. We suggest that threshold corrections to the classical gauge coupling function could solve these problems.

String unification, universal one-loop corrections and strongly coupled heterotic string theory

We derive the universal threshold corrections in heterotic string theory including a continuous Wilson line. Unification of gauge and gravitational couplings is shown to be possible even within perturbative string theory. The relative importance of gauge group dependent and independent thresholds on unification is clarified. Equipped with these results we can then attempt an extrapolation to the strongly coupled heterotic string — M-theory. We argue that such an extrapolation might be meaningful because of the holomorphic structure of the gauge coupling function and the close connection of the threshold corrections to the anomaly cancellation mechanism.

Coping with strongly coupled string theory.

String theory, if it describes nature, is probably strongly coupled. As a result, one might despair of making any statements about the theory. In the framework of a set of clearly spelled out assumptions, we show that this is not necessarily the case. Certain discrete gauge symmetries, combined with supersymmetry, tightly constrain the form of the effective action. Among our assumptions are that the true ground state can be obtained from some perturbative ground state by varying the coupling, and that the actual numerical value of the low energy field theoretic coupling ${g^2 \over 4\pi}$ is small. It follows that the low energy theory is approximately supersymmetric; corrections to the superpotential and gauge coupling function are small, while corrections to the Kahler potential are large; the spectrum of light particles is the same at strong as at weak coupling. We survey the phenomenological consequences of this viewpoint. We also note that the string axion can serve as QCD axion in this framework (modulo cosmological problems).

Some explorations in holomorphy.

In supersymmetric theories, one can obtain striking results and insights by exploiting the fact that the superpotential and the gauge coupling function are holomorphic functions of the model parameters. The precise meaning of this holomorphy is subtle, and has been explained most clearly by Shifman and Vainshtein, who have stressed the role of the Wilsonian effective action. In this note, we elaborate on the Shifman-Vainshtein program, applying it to examples in grand unification, supersymmetric QCD and string theory. We stress that among the ``model parameters" are the cutoffs used to define the Wilsonian action itself, and that generically these must be defined in a field-dependent manner to obtain holomorphic results.

TOWARDS FINITENESS WITHOUT SUPERSYMMETRY

Some aspects of finite quantum field theories in 3+1 dimensions are discussed. A model with nonsupersymmetric particle content and vanishing one- and two-loop beta functions for the gauge coupling and one-loop beta functions for Yukawa couplings is presented.

Supergravity and matter: linear multiplet couplings and Kähler anomaly cancellation

We present in detail the properties of a linear multiplet in interaction with supergravity and matter, with a special emphasis on the coupling of Chern-Simons forms, relevant for the problem of the chiral and conformal anomalies in relation with Kähler transformations and the corresponding anomaly cancellations. The linear supermultiplet describes an antisymmetric tensor gauge field together with a dilaton and a Majorana spinor. In particular, these fields are found among the massless modes of superstring theories. We review the general properties of this supermultiplet in the Kähler superspace formalism and construct the complete supersymmetric action. This includes the classically Kähler invariant component field action for all the kinetic terms as well as a Green-Schwarz type action which exhibits a non-holomorphic gauge coupling function.

Linear supermultiplets and non-holomorphic gauge coupling functions

We construct the general couplings of linear multiplets, including Chern-Simons forms, to chiral matter as well as to the standard supergravity-matter system. Insisting on a canonically normalized Einstein term we discuss in particular the appearance of non-holomorphic gauge couplings and perform duality transformations in full generality. We present the implications of these structures for the effective description of sigma model anomalies, with and without coupling to supergravity, following recent proposals of Derendinger, Ferrara, Kounnas and Zwirner and of Cardoso and Ovrut.