Four-dimensional Effective Theory Research Articles

An algebraic classification of exceptional EFTs

We classify four-dimensional effective field theories (EFTs) with enhanced soft limits, which arise due to non-linearly realised symmetries on the Goldstone modes of such theories. We present an algorithm for deriving all possible algebras that can be non-linearly realised on a set of Goldstone modes with canonical propagators, linearly realised Poincaré symmetries and interactions at weak coupling. An important ingredient in our analysis is inverse Higgs trees which systematically incorporate the requirements for the existence of inverse Higgs constraints. These are the algebraic cousin of the on-shell soft data one provides for soft bootstrapping EFTs. We perform full classifications for single scalar and multiple spin-1/2 fermion EFTs and present a thorough analysis for multiple scalars. In each case there are only a small number of algebras consistent with field-dependent transformation rules, leading to the class of exceptional EFTs including the scalar sector of Dirac-Born-Infeld, Special Galileon and Volkov-Akulov theories. We also discuss the coupling of a U(1) gauge vector to the exceptional scalar theories, showing that there is a Special Galileon version of the full Dirac-Born-Infeld theory. This paper is part I in a series of two papers, with the second providing an algebraic classification of supersymmetric theories with non-linearly realised symmetries.

Zero-mode product expansions and higher-order couplings in gauge backgrounds

We study a four-dimensional low-energy effective field theory derived from extra dimensional field theories with general gauge backgrounds. We find that products among fermionic zero-modes and lightest scalar modes are expanded by other fermionic zero-modes and lightest scalar modes. Using this aspect, we show that higher-order couplings among the fermionic zero-modes and the lightest scalar mode can be decomposed into three-point couplings. This selection rule originating from a structure of the Dirac-type operators indicates the operator product expansion the underlying conformal field theory.

New black-string solutions for an anti–de Sitter brane in scalar-tensor gravity

We consider a five-dimensional theory with a scalar field non-minimally-coupled to gravity, and we look for novel black-string solutions in the bulk. By appropriately choosing the non-minimal coupling function of the scalar field, we analytically solve the gravitational and scalar-field equations in the bulk to produce black-string solutions that describe a Schwarzschild-Anti-de Sitter space-time on the brane. We produce two complete such solutions that are both characterised by a regular scalar field, a localised-close-to-our brane energy-momentum tensor and a negative-definite, non-trivial bulk potential that may support by itself the warping of the space-time even in the absence of the traditional, negative, bulk cosmological constant. Despite the infinitely-long string singularity in the bulk, the four-dimensional effective theory on the brane is robust with the effective gravity scale being related to the fundamental one and the warping scale. It is worth noting that if we set the mass of the black hole on the brane equal to zero, the black string disappears leaving behind a regular brane-world model with only a true singularity at the boundary of the fifth dimension.

Tidal Love numbers of black holes and neutron stars in the presence of higher dimensions: Implications of GW170817

We calculate the tidal Love numbers of black holes and neutron stars in the presence of higher dimensions. The perturbation equations around an arbitrary static and spherically symmetric metric for the even-parity modes are presented in the context of an effective four-dimensional theory on the brane. This subsequently leads to the desired expression for the tidal Love number for black holes in the presence of extra spatial dimensions. Surprisingly, these numbers are nonzero and (more importantly) negative. We extend our method to determine the tidal Love number of neutron stars in a spacetime inheriting extra dimensions and show that, in the context of effective gravitational theory on the brane, they are smaller than in general relativity. Finally, we explicitly demonstrate that earlier constraints on the parameters inherited from higher dimensions are consistent with the bound on the tidal deformability parameter from the GW170817 event as well.

Cosmological model due to dimensional reduction of higher-dimensional massive gravity theory

We investigate a cosmological model resulting from a dimensional reduction of the higher-dimensional dRGT massive gravity. By using the Kaluza-Klein dimensional reduction, we obtain an effective four-dimensional massive gravity theory with a scalar field. It is found that the resulting theory corresponds to a combined description of mass-varying massive gravity and quasi-dilaton massive gravity. By analyzing the cosmological solution, we found that it is possible to obtain the late-time expansion of the universe due to the graviton mass. By using a dynamical system approach, we found regions of model parameters for which the late-time expansion of the universe is a stable fixed point.

Mathcal{N}=1 superfield description of BPS solutions in 6D gauged SUGRA with 3-branes

We provide mathcal{N}=1 superfield description of BPS backgrounds in six-dimensional supergravity (6D SUGRA) with 3-branes, which is compactified on a two-dimensional space. The brane terms induce the localized fluxes. We find a useful gauge in which the background equations become significantly simple. This is not the Wess-Zumino gauge, and the relation to the usual component-field expression of 6D SUGRA is not straightforward. One of the equations reduces to the Liouville equation. By moving to the Wess-Zumino gauge, we check that our expressions reproduce the known results of the previous works, which are expressed in the component fields. Our results help us develop the systematic derivation of four-dimensional effective theories that keeps the mathcal{N}=1 SUSY structure.

Flux compactifications and naturalness

Free massless scalars have a shift symmetry. This is usually broken by gauge and Yukawa interactions, such that quantum corrections induce a quadratically divergent mass term. In the Standard Model this leads to the hierarchy problem of the electroweak theory, the question why the Higgs mass is so much smaller than the Planck mass. We present an example where a large scalar mass term is avoided by coupling the scalar to an infinite tower of massive states which are obtained from a six-dimensional theory compactified on a torus with magnetic flux. The series of divergent quantum corrections adds up to zero, and we show explicitly that the shift symmetry of the scalar is preserved in the effective four-dimensional theory despite the presence of gauge and Yukawa interaction terms.

Orientifolds and duality cascades: confinement before the wall

We consider D-branes at orientifold singularities and discuss two properties of the corresponding low energy four-dimensional effective theories which are not shared, generically, by other Calabi-Yau singularities. The first property is that duality cascades are finite and, unlike ordinary ones, do not require an infinite number of degrees of freedom to be UV-completed. The second is that orientifolds tend to stabilize runaway directions. These two properties can have interesting implications and widen in an intriguing way the variety of gauge theories one can describe using D-branes.

Three-forms in supergravity and flux compactifications

We present a duality procedure that relates conventional four-dimensional matter-coupled mathcal{N}=1 supergravities to dual formulations in which auxiliary fields are replaced by field strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the superpotential to vacuum expectation values of the field strengths. We then apply this general duality to type IIA string compactifications on Calabi–Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms.

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of {mathbb{Z}}_2times {mathbb{Z}}_2 . Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the cfour-dimensional theory.

Constrained superfields on metastable anti-D3-branes

We study the effect of brane polarization on the supersymmetry transformations of probe anti-D3-branes at the tip of a Klebanov-Strassler throat geometry. As is well known, the probe branes can polarize into NS5-branes and decay to a supersymmetric state by brane-flux annihilation. The effective potential has a metastable minimum as long as the number of anti-D3-branes is small compared to the number of flux quanta. We study the reduced four-dimensional effective NS5-brane theory and show that in the metastable minimum supersymmetry is non-linearly realized to leading order, as expected for spontaneously broken supersymmetry. However, a strict decoupling limit of the higher order corrections in terms of a standard nilpotent superfield does not seem to exist. We comment on the possible implications of these results for more general low-energy effective descriptions of inflation or de Sitter vacua.

On four-derivative terms in IIB Calabi-Yau orientifold reductions

We perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational α′3-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of O3/O7-planes. We consider infinitesimal Kähler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the Kähler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inflation.

Modular symmetry in magnetized/intersecting D-brane models

We study the modular symmetry in four-dimensional low-energy effective field theory, which is derived from type IIB magnetized D-brane models and type IIA intersecting D-brane models. We analyze modular symmetric behaviors of perturbative terms and non-perturbative terms induced by D-brane instanton effects. Anomalies are also investigated and such an analysis on anomalies suggests corrections in effective field theory.

Warped K\xe4hler potentials and fluxes

The four-dimensional effective theory for type IIB warped flux compactifications proposed in [1] is completed by taking into account the backreaction of the Kähler moduli on the three-form fluxes. The only required modification consists in a flux-dependent contribution to the chiral fields parametrising the Kähler moduli. The resulting supersymmetric effective theory satisfies the no-scale condition and consistently combines previous partial results present in the literature. Similar results hold for M-theory warped compactifications on Calabi-Yau fourfolds, whose effective field theory and Kähler potential are also discussed.

A note on gauge-fixing in the electroweak sector of non-minimal UED

Electroweak observables are highly sensitive to the loop corrections. Therefore, a proper gauge-fixing mechanism is always needed to define the propagators which are involved in Feynman loop amplitude. With this spirit, we compute gauge-fixing mechanism in five-dimensional (5D) universal extra-dimensional (UED) model with boundary localized terms (BLTs). These BLTs are not 5D operators in four-dimensional (4D) effective theory but some sort of boundary conditions on the respective fields at the fixed points of [Formula: see text] orbifold. Furthermore, these BLTs nontrivially modify the Kaluza–Klein (KK) spectra and some of the interactions among the KK-excitations compared to the minimal UED (mUED), in which, these BLTs are absent. In this note, we calculate the gauge-fixing mechanism in the electroweak sector of such nontrivial UED scenario. Moreover, we discuss the composition and masses of Goldstone and any physical scalar that emerge after the symmetry breaking in this set up with different choices of gauge.

Prospects for primordial gravitational waves in string inflation

Assuming that the early universe had (i) a description using perturbative string theory and its field theory limit, (ii) an epoch of slow-roll inflation within a four-dimensional effective field theory and a hierarchy of scales [Formula: see text] that keeps the latter under control, we derive an upper bound on the amplitude of primordial gravitational waves. The bound is very sensitive to mild changes in numerical coefficients and the expansion parameters. For example, allowing couplings and mass-squared hierarchies [Formula: see text] implies [Formula: see text], but asking more safely for hierarchies [Formula: see text], the bound becomes [Formula: see text]. Moreover, large volumes — typically used in string models to keep backreaction and moduli stabilization under control — drive [Formula: see text] down. Consequently, any detection of inflationary gravitational waves would present an interesting but difficult challenge for string theory.

Dynamical supersymmetry breaking on magnetized tori and orbifolds

We construct several dynamical supersymmetry breaking (DSB) models within a single ten-dimensional supersymmetric Yang–Mills (SYM) theory, compactified on magnetized tori with or without orbifolding. We study the case that the supersymmetry breaking is triggered by a strong dynamics of SU(NC) SYM theory with NF flavors contained in the four-dimensional effective theory. We show several configurations of magnetic fluxes and orbifolds, those potentially yield, below the compactification scale, the field contents and couplings required for triggering DSB. We especially find a class of self-complete DSB models on orbifolds, where all the extra fields are eliminated by the orbifold projection and DSB successfully occurs within the given framework. Comments on some perspectives for associating the obtained DSB models with the other sectors, such as the visible sector and another hidden sector for, e.g., stabilizing moduli, are also given.

Fermions in five-dimensional brane world models

In the present paper the fermion fields, living in the background of five-dimensional warped brane world models with compact extra dimension, are thoroughly examined. The Kaluza-Klein decomposition and isolation of the physical degrees of freedom is performed for those five-dimensional fermion field Lagrangians, which admit such a decomposition to be performed in a mathematically consistent way and provide a physically reasonable four-dimensional effective theory. It is also shown that for the majority of five-dimensional fermion field Lagrangians there are no (at least rather obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover, in these cases one may expect the appearance of various pathologies in the four-dimensional effective theory. Among the cases, for which the Kaluza-Klein decomposition can be performed in a mathematically consistent way, the case, which reproduces the Standard Model by the zero Kaluza-Klein modes most closely regardless of the size of the extra dimension, is examined in detail in the background of the Randall-Sundrum model.

Holographic effective field theories

We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.

Bigravity from gradient expansion

We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.