Cancellation Of Gravitational Anomalies Research Articles

On the frozen F-theory landscape

We study 6d \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = (1, 0) supergravity theories arising in the frozen phase of F-theory. For each of the known global models, we construct an F-theory compactification in the unfrozen phase with an identical non-abelian gauge algebra and massless matter content. Two such low energy effective theories are then distinguished through gauge enhancements in moduli space. We study potentially new global models obtained via compact embeddings of a plethora of 6d \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = (1, 0) superconformal field theories and little string theories constructed using frozen 7-branes. In some cases, these provably do not exist, and in other cases, we explicitly construct a compact embedding, yielding 6d supergravity theories with new massless spectra. Finally, by using gravitational anomaly cancellation, we conjecture the existence of localized neutral hypermultiplets along frozen 7-brane loci.

Anomaly cancellation in string theory

The anomaly cancellation in superstring theory is known to hold at leading order in the curvature for the gauge groups [Formula: see text] and [Formula: see text]. The coefficients of the next-to-leading order terms may be evaluated, and a mechanism for cancellation is described, which would remain valid at higher genus when there exists a global splitting of the coordinates of supermoduli space. Since the spin-[Formula: see text] fields transform under the adjoint representation in these models, compactification of the heterotic string over [Formula: see text] or a fundamental 12-dimensional theory, from which superstrings are produced through an elliptic fibration, over [Formula: see text], provides another phenomenologically viable theory at lower energies compatible with the standard description of the elementary particle interactions. The 96 spin-[Formula: see text] fields now would transform under the fundamental representation of [Formula: see text] and the spin-one gauge fields would belong to the adjoint representation. The sum of the anomaly polynomials for the particle content of the [Formula: see text] model vanishes at [Formula: see text]. The contributions to the gravitational anomaly from the particles and antiparticles cancel by the CPT theorem and the duality transformations of polynomials of degree 6 in the curvature and the field strength. The existence of the interaction of a spin-2 charge, which is conserved only over a finite time interval, can be traced to nonlocal terms in the reduction of the string field theory to the gravitational sector. The source of the global gravitational anomaly cancellation in the modular form equations derived from an elliptic fibration of a 12-dimensional theory would restrict the compactifications and provide a method for preserving the absence of anomalies in four dimensions.

Elliptic Calabi-Yau fivefolds and 2d (0,2) F-theory landscape

In this paper, we initiate the study of the 2d F-theory landscape based on compact elliptic Calabi-Yau fivefolds. In particular, we determine the boundary models of the landscape using Calabi-Yau fivefolds with the largest known Hodge numbers h1,1 and h4,1. The former gives rise to the largest geometric gauge group in the currently known 2d (0,2) supergravity landscape, which is {E}_8^{482;632;421}times {F}_4^{3;224;195;728}times {G}_2^{11;927;989;964}times mathrm{SU}{(2)}^{25;625;222;180} . Besides that, we systematically study the hypersurfaces in weighted projective spaces with small degrees, and check the gravitational anomaly cancellation. Moreover, we also initiate the study of singular bases in 2d F-theory. We find that orbifold singularities on the base fourfold have non-zero contributions to the gravitational anomaly.

Gravitational and chiral anomalies in the running vacuum universe and matter-antimatter asymmetry

We present a model for the Universe in which quantum anomalies are argued to play an important dual role: they are responsible for generating matter-antimatter asymmetry in the cosmos, but also provide time-dependent contributions to the vacuum energy density of ``running-vacuum'' type, which drive the Universe's evolution. According to this scenario, during the inflationary phase of a string-inspired Universe, and its subsequent exit, the existence of primordial gravitational waves induces gravitational anomalies, which couple to the [Kalb-Ramond (KR)] axion field emerging from the antisymmetric tensor field of the massless gravitational multiplet of the string. Such anomalous $CP$-violating interactions have two important effects. First, they lead to contributions to the vacuum energy density of the form appearing in the ``running vacuum model'' (RVM) framework, which are proportional to both, the square and the fourth power of the effective Hubble parameter, ${H}^{2}$ and ${H}^{4}$ respectively. The ${H}^{4}$ terms may lead to inflation, in a dynamical scenario whereby the role of the inflaton is played by the effective scalar-field (``vacuumon'') representation of the RVM. Second, there is an undiluted KR axion at the end of inflation, which plays an important role in generating matter-antimatter asymmetry in the cosmos, through baryogenesis via leptogenesis in models involving heavy right-handed neutrinos. As the Universe exits inflation and enters a radiation-dominated era, the generation of chiral fermionic matter is responsible for the cancellation of gravitational anomalies, thus restoring diffeomorphism invariance for the matter/radiation (quantum) theory, as required for consistency. Chiral U(1) anomalies may remain uncompensated, though, during matter/radiation dominance, providing RVM-like ${H}^{2}$ and ${H}^{4}$ contributions to the Universe energy density. Finally, in the current era, when the Universe enters a de Sitter phase again, and matter is no longer dominant, gravitational anomalies resurface, leading to RVM-like ${H}^{2}$ contributions to the vacuum energy density, which are however much more suppressed, as compared to their counterparts during inflation, due to the smallness of the present era's Hubble parameter ${H}_{0}$. In turn, this feature endows the observed dark energy with a dynamical character that follows the RVM pattern, a fact which has been shown to improve the global fits to the current cosmological observations as compared to the concordance $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model with its rigid cosmological constant, $\mathrm{\ensuremath{\Lambda}}>0$. Our model favors axionic dark matter, the source of which can be the KR axion. The uncompensated chiral anomalies in late epochs of the Universe are argued to play an important role in this, in the context of cosmological models characterized by the presence of large-scale cosmic magnetic fields at late eras.

Global gravitational anomaly cancellation for five-branes

We show that the global mixed gauge-gravitational anomaly of the worldvolume theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken into account. This result extends to the type IIA and heterotic $E_8 \times E_8$ five-branes. As a by-product, we provide a definition of the chiral fermionic fields for generic non-spin M5-brane worldvolume and determine the coupling between the self-dual field and the M-theory C-field.

Gravitational anomaly cancellation and modular invariance

In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $4k+2$ dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaum\'e and Witten in dimensions 2, 6 and 10 (\cite{AW}) as special cases. In dimension $4k+1$, we derive anomaly cancellation formulas for index gerbes. In dimension $4k+3$, we obtain certain results about eta invariants, which are interesting in spectral geometry.

Higher order terms in an improved heteroticM-theory

Curvature-squared terms are added to a consistent formulation of supergravity on manifolds with boundary which is meant to represent the low energy limit of strongly coupled heterotic string theory. These terms are necessary for the cancellation of gravitational anomalies and for reductions to lower dimensions with broken chiral symmetry. The consequences of anomaly cancellation when flux and extrinsic curvature terms are taken into account have yet to be fully exploited, but some implications for flux terms are discussed here.

Hawking radiation from rotating black holes and gravitational anomalies

We study the Hawking radiation from Rotating black holes from gravitational anomalies point of view. First, we show that the scalar field theory near the Kerr black hole horizon can be reduced to the 2-dimensional effective theory. Then, following Robinson and Wilczek, we derive the Hawking flux by requiring the cancellation of gravitational anomalies. We also apply this method to Hawking radiation from higher dimensional Myers-Perry black holes. In the Appendix, we present the trace anomaly derivation of Hawking radiation to argue the validity of the boundary condition at the horizon.

Gravitational anomaly cancellation for $M$-theory fivebranes

We study gravitational anomalies for fivebranes in M theory. We show that an apparent anomaly in diffeomorphisms acting on the normal bundle is cancelled by a careful treatment of the M theory Chern-Simons coupling in the presence of fivebranes. One interesting aspect of our treatment is the way in which a magnetic object (the fivebrane) is smoothed out through coupling to gravity and the resulting relation between antisymmetric tensor gauge transformations and diffeomorphisms in the presence of a fivebrane.

Orbifolds of M-theory

We study Z 2 -orbifolds of 11-dimensional M-theory on tori of various dimensions. The most interesting model (besides the known S 1/ Z 2 case) corresponds to T 5/ Z 2 for which we argue that the resulting six-dimensional theory is equivalent to the type IIB string compactified on K3. Gravitational anomaly cancellation plays a crucial role in determining what states appear in the twisted sector. Most of the other models appear to break spacetime supersymmetry. We observe that M-theory tends to produce chiral compactifications on orbifolds, and that our results may provide an insight into the mechanism by which twisted-sector states arise in this hypothetical theory.

Gauge and gravitational anomaly cancellation in type-I superstring theory

We present a comprehensive study of the gauge, mixed and gravitational anomalies in the type-I open superstring theory using the covariant RNS operator formalism. All anomalies are shown to cancel among the possible one-loop open string diagrams for the gauge group SO(32). Furthermore, we clear up some points that may not have been completely understood in the past and show how the anomaly contributions arise from the boundaries of moduli space. We also discuss how the open string calculations can be understood in the boundary and crosscap formalism.

Cancellation of gravitational anomalies in d=6 supergravities

The conditions for cancellation of gravitational anomalies in d=6 chiral supergravities based on the systematic use of index theorems are examined here. The authors point out the minimal necessary combinations of chiral fermions (with spin 3/2 and 1/2) and (anti-) self-dual antisymmetric tensors, as well as the corresponding combinations of N=1, d=6 supermultiplets that ensure cancellation of gravitational anomalies.

Anomaly cancellation in ten dimensions and beyond

A new mechanism to turn Green-Schwarz gauge anomaly cancellation into complete gravitational anomaly cancellation is discussed. It can be used to derive the type IIB cancellations in d = 10 and d = 18 without explicit calculations and also to derive new complete cancellations involving two-form spinors in d = 10 and d = 14. Also new Green-Schwarz cancellations are obtained for E 7 in d = 14 and SO( d−2) for arbitrary even d. Some aspects of compactification are also discussed.

A preon model with family-replication from a D = 6, N = 2 supergravity theory

The gauge structure E 7 × U(1) × E 6 has recently been suggested in connection with a D = 6, N = 2 supergravity theory owing to its remarkable property of gauge and gravitational anomaly-cancellation. It is shown that the identification of the four-dimensional massless spin- 1 2 fields arising from this gauge structure with preons, rather than with quarks and leptons, can lead to a desirable preonic spectrum which has recently been suggested by one of us and which predicts foru composite quark-lepton families. By contrast, an identification of the same massless fields with quarks and leptons would yield only two families. A few other alternative gauge structures are discussed.