Low-energy Effective Action Research Articles

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.

Superconformal $ \mathcal{N} = {3} $ SYM low-energy effective action

We construct a manifestly $ \mathcal{N} = {3} $ supersymmetric low-energy effective action of $ \mathcal{N} = {3} $ super Yang-Mills theory. The effective action is written in the $ \mathcal{N} = {3} $ harmonic superspace and respects the full $ \mathcal{N} = {3} $ superconformal symmetry. On mass shell this action is responsible for the four-derivative terms in the $ \mathcal{N} = {4} $ SYM effective action, such as F 4/X 4 and its supersymmetric completions, while off shell it involves also higher- derivative terms. For constant Maxwell and scalar fields its bosonic part coincides, up to the F 6/X 8 order, with the bosonic part of the D3 brane action in the AdS5 × S 5 background. We also argue that in the sector of scalar fields it involves the correctly normalized Wess-Zumino term with the implicit SU(3) symmetry.

Stringy instantons in SU(N) $ \mathcal{N} = {2} $ non-conformal gauge theories

In this paper we explicitly obtain the leading corrections to the SU(N) N=2 prepotential due to stringy instantons both in flat space-time and in the presence of a non-trivial graviphoton background field. We show that the stringy corrections to the prepotential are expressible in terms of the elementary symmetric polynomials. For N>2 the theory is not conformal; we discuss the introduction of an explicit dependence on the string scale \alpha' in the low-energy effective action through the stringy non-perturbative sector.

The background field method for $ \mathcal{N} = {2} $ , d3 super Chern-Simons-matter theories

We develop the superfield background field method and study the effective action in the N=2, d3 supersymmetric Chern-Simons-matter systems. The one-loop low-energy effective action for non-Abelian supersymmetric Chern-Simons theory is computed to order $F^4$ by use of N = 2 superfield heat kernel techniques.

Role of space-time foam in breaking supersymmetry via the Barbero-Immirzi parameter

We discuss how: (i) a dilaton/axion superfield can play the role of a Barbero-Immirzi field in four-dimensional conformal quantum supergravity theories, (ii) a fermionic component of such a dilaton/axion superfield may play the role of a Goldstino in the low-energy effective action obtained from a superstring theory with $F$-type global supersymmetry breaking, (iii) this global supersymmetry breaking is communicated to the gravitational sector via the supergravity coupling of the Goldstino, and (iv) such a scenario may be realized explicitly in a D-foam model with D-particle defects fluctuating stochastically.

Bi-harmonic superspace for $ \mathcal{N} = 4 $ d = 4 super Yang-Mills

We develop \( \mathcal{N} = 4 \) d = 4 bi-harmonic superspace and use it to derive a novel form for the low-energy effective action in \( \mathcal{N} = 4 \) super Yang-Mills theory. We solve the \( \mathcal{N} = 4 \) supergauge constraints in this superspace in terms of analytic superfields. Using these superfields, we construct a simple functional that respects \( \mathcal{N} = 4 \) supersymmetry and scale invariance. In components, it reproduces all on-shell terms in the four-derivative part of the \( \mathcal{N} = 4 \) SYM effective action; in particular, the F 4/X 4 and Wess-Zumino terms. The latter comes out in a novel SO(3) × SO(3)-invariant form.

Enhanced instability of de Sitter space in Einstein-Gauss-Bonnet gravity

We show that the addition of a topological Gauss-Bonnet term to the gravitational action can greatly increase the instability of four-dimensional de Sitter space, by favoring the nucleation of black holes. The pair-production rate given by the Euclidean action for the instanton takes the form exp(Delta S) where S is the entropy in Einstein-Gauss-Bonnet theory. The coefficient of the Gauss-Bonnet term in the action sets a stability bound on the curvature of empty de Sitter space. For that coefficient in the low-energy effective action of heterotic string theory, the maximal curvature of de Sitter space is in general much lower than the Planck scale.

Stringy differential geometry, beyond Riemann

While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also O(D,D) T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry which is given by a direct product of two local Lorentz groups, SO(1,D-1) times SO(1,D-1). We comment that the notion of cosmological constant naturally changes.

The $ \mathcal{N} = 4 $ effective action of type IIA supergravity compactified on SU(2)-structure manifolds

We study compactifications of type IIA supergravity on six-dimensional manifolds with SU(2) structure and compute the low-energy effective action in terms of the non-trivial intrinsic torsion. The consistency with gauged N=4 supergravity is established and the gauge group is determined. Depending on the structure of the intrinsic torsion, antisymmetric tensor fields can become massive.

Higher-derivative supersymmetric gauge theory

We study the one-loop low-energy effective action for the higher-derivative superfield gauge theory coupled to a chiral matter.

The effective action of D6-branes in $ \mathcal{N} = 1 $ type IIA orientifolds

We use a Kaluza-Klein reduction to compute the low-energy effective action for the massless modes of a spacetime-filling D6-brane wrapped on a special Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold. The modifications to the characteristic data of the $ \mathcal{N} = 1 $ bulk orientifold theory in the presence of a D6-brane are analysed by studying the underlying Type IIA supergravity coupled to the brane world volume in the democratic formulation and performing a detailed dualisation procedure. The $ \mathcal{N} = 1 $ chiralcoordinates are found to be in agreement with expectations from mirror symmetry. We work out the Kähler potential for the chiral superfields as well as the gauge kinetic functions for the bulk and the brane gauge multiplets including the kinetic mixing between the two. The scalar potential resulting from the dualisation procedure can be formally interpreted in terms of a superpotential. Finally, the gauging of the Peccei-Quinn shift symmetries of the complex structure multiplets reproduces the D-term potential enforcing the calibration condition for special Lagrangian 3-cycles.

Collective modes in the color flavor-locked phase

We study the low-energy effective action for some collective modes of the color flavor-locked (CFL) phase of QCD. This phase of matter has long been known to be a superfluid because by picking a phase its order parameter breaks the quark-number U(1)B symmetry spontaneously. We consider the modes describing fluctuations in the magnitude of the condensate, namely the Higgs mode, and in the phase of the condensate, namely the Nambu–Goldstone (NG) (or Anderson–Bogoliubov) mode associated with the breaking of U(1)B. By employing as microscopic theory the Nambu–Jona-Lasinio model, we reproduce known results for the Lagrangian of the NG field to the leading order in the chemical potential and extend such results evaluating corrections due to the gap parameter. Moreover, we determine the interaction terms between the Higgs and the NG field. This study paves the way for a more reliable study of various dissipative processes in rotating compact stars with a quark matter core in the CFL phase.

Wess-Zumino term in the $ \mathcal{N} = 4 $ SYM effective action revisited

The low-energy effective action for the N=4 super Yang-Mills on the Coulomb branch is known to include an SO(6)-invariant Wess-Zumino (WZ) term for the six scalar fields. For each maximal, non-anomalous subgroup of the SU(4) R-symmetry, we find a four-dimensional form of the WZ term with this subgroup being manifest. We then show that a recently proposed expression for the four-derivative part of the effective action in N=4 USp(4) harmonic superspace yields the WZ term with manifest SO(5) R-symmetry subgroup. The N=2 SU(2) harmonic superspace form of the effective action produces the WZ term with manifest SO(4) x SO(2). We argue that there is no four-dimensional form of the WZ term with manifest SU(3) R-symmetry, which is relevant for N=1 and N=3 superspace formulations of the effective action.

Optical-lattice Hamiltonians for relativistic quantum electrodynamics

We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in 1+1, 2+1 and 3+1 dimensions whose low energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to 2+1 dimensional electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.

Quantum-gravity induced Lorentz violation and dynamical mass generation

In Ref. [1] (by J. Alexandre) a minimal extension of (3+1)-dimensional Quantum Electrodynamics has been proposed, which includes Lorentz-Violation (LV) in the form of higher-(spatial)-derivative isotropic terms in the gauge sector, suppressed by a mass scale $M$. The model can lead to dynamical mass generation for charged fermions. In this article I elaborate further on this idea and I attempt to connect it to specific quantum-gravity models, inspired from string/brane theory. Specifically, in the first part of the article, I comment briefly on the gauge dependence of the dynamical mass generation in the approximations of [1], and I propose a possible avenue for obtaining the true gauge-parameter-independent value of the mass by means of Pinch Technique argumentations. In the second part of the work I embed the LV QED model into multibrane world scenarios with a view to provide a geometrical way of enhancing the dynamical mass to phenomenologically realistic values by means of bulk warp metric factors, in an (inverse) Randall-Sundrum hierarchy. Finally in the third part of this note, I demonstrate that such Lorentz Violating QED models may represent parts of a low-energy effective action (of Finsler-Born-Infeld type) of open strings propagating in quantum D0-particle stochastic space-time foam backgrounds, which are viewed as consistent quantum gravity configurations.

Spin-one color superconductors: Collective modes and effective Lagrangian

We investigate the collective excitations in spin-one color superconductors. We classify the Nambu–Goldstone modes by the pattern of spontaneous symmetry breaking, and then use the Ginzburg–Landau theory to derive their dispersion relations. These soft modes play an important role for the low-energy dynamics of the system such as the transport phenomena and hence are relevant for late-stage evolution of neutron stars. In the case of the color-spin-locking phase, we use a functional technique to obtain the low-energy effective action for the physical Nambu–Goldstone bosons that survive after gauging the color symmetry.

Low-energy effective actions in three-dimensional extended SYM theories

We develop the background field method in the \( \mathcal{N} = 2 \), d = 3 superspace for studying effective actions in three-dimensional SYM models which live in the world-volume of various 2-branes. In particular, the low-energy effective action for the \( \mathcal{N} = 2 \) quiver gauge theory with four chiral superfields in the bifundamental representation is calculated and studied. This gauge theory describes a D2 brane probing the conifold singularity. Surprisingly, the scale-invariant part of this effective action coincides with the classical action of the Abelian ABJM theory. Apart from this \( \mathcal{N} = 2 \) quiver gauge theory we study the low-energy effective action in pure \( \mathcal{N} = 2 \), \( \mathcal{N} = 4 \) and \( \mathcal{N} = 8 \) SYM theories with gauge group SU(N) spontaneously broken down to an Abelian subgroup. In particular, for the \( \mathcal{N} = 4 \) SYM we find similar correspondence between its one-loop effective action and the classical action of the Abelian Gaiotto-Witten theory.

T-Duality versus Gauge Symmetry

We review the recently constructed `double field theory' which introduces in addition to the conventional coordinates associated to momentum modes coordinates associated to winding modes. Thereby, T-duality becomes a global symmetry of the theory, which can be viewed as an `O(D,D) covariantization' of the low-energy effective space-time action of closed string theory. We discuss its symmetries with a special emphasis on the relation between global duality symmetries and local gauge symmetries.

On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds

We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT-like and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the properties observed in our concrete models, which tend to be missed when only “generic” features of a model are assumed. We search for interesting vacua and find several de Sitter solutions, but so far, they all turn out to be unstable.

On the effective theory of long open strings

We study the general low-energy effective action on long open strings, such as confining strings in pure gauge theories. Using Lorentz invariance, we find that for a string of length R, the leading deviation from the Nambu-Goto energy levels generically occurs at order 1/R^4 (including a correction to the ground state energy), as opposed to 1/R^5 for excited closed strings in four dimensions, and 1/R^7 for closed strings in three dimensions. This is true both for Dirichlet and for Neumann boundary conditions for the transverse directions, though the worldsheet boundary actions are different. The Dirichlet case is relevant (for instance) for the force between external quarks in a confining gauge theory, and the Neumann case for a string stretched between domain walls. In the specific case of confining gauge theories with a weakly curved holographic dual, we compute the coefficient of the leading correction when the open string ends on two D-branes, and find a non-vanishing result.