Nonlocal Effective Action Research Articles

Anomaly mediated gaugino mass and path-integral measure

In recent years, there have been controversy concerning the anomaly mediated gaugino mass in the superspace formalism of supergravity. In this paper, we reexamine the gaugino mass term in this formalism by paying particular attention to symmetry which controls gaugino masses in supergravity. We first discuss super-Diffeomorphism invariance of path-integral measures of charged superfields. As we will show, the super-Diffeomorphism invariant measure is not invariant under a super-Weyl transformation, which is the origin of the anomaly mediated gaugino mass. We show how the anomaly mediated gaugino mass is expressed as a local operator in a Wilsonian effective action in a super-Diffeomorphism covariant way. We also obtain a gaugino mass term independent of the gauge choice of the fictitious super-Weyl symmetry in the super-Weyl compensator formalism, which reproduces the widely accepted result. Besides, we discuss how to reconcile the gaugino mass term in the local Wilsonian effective action and the gaugino mass term appearing in a non-local 1PI quantum effective action.

A caveat on building nonlocal models of cosmology

Nonlocal models of cosmology might derive from graviton loop corrections to the effective field equations from the epoch of primordial inflation. Although the Schwinger-Keldysh formalism would automatically produce causal and conserved effective field equations, the models so far proposed have been purely phenomenological. Two techniques have been employed to generate causal and conserved field equations: either varying an invariant nonlocal effective action and then enforcing causality by the ad hoc replacement of any advanced Green's function with its retarded counterpart, or else introducing causal nonlocality into a general ansatz for the field equations and then enforcing conservation. We point out here that the two techniques access very different classes of models, and that neither one of them may represent what would actually arise from fundamental theory.

INCONSISTENCIES FROM A RUNNING COSMOLOGICAL CONSTANT

We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation, where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the nonlocal effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem.

Super-Weyl anomalies in $ \mathcal{N} $ = 2 supergravity and (non)local effective actions

Using the formulation for N=2 conformal supergravity in SU(2) superspace, we define super-Weyl (or superconformal) anomalies and construct two types of nonlocal effective actions that generate these anomalies. We also present the local Wess-Zumino action for spontaneously broken N=2 superconformal symmetry, with the Goldstone supermultiplet identified with a reduced chiral superfield containing the dilaton and the axion among its components.

Entropy and temperature from black-hole/near-horizon-CFT duality

We construct a two-dimensional CFT, in the form of a Liouville theory, in the near-horizon limit of four- and three-dimensional black holes. The near-horizon CFT assumes two-dimensional black hole solutions first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088–104) and expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two-dimensional black holes admit a Diff(S1) subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. This charge and the lowest Virasoro eigen-mode reproduce the correct Bekenstein–Hawking entropy of the four- and three-dimensional black holes via the known Cardy formula (Blöte et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two-dimensional CFT's energy–momentum tensor is anomalous. However, in the horizon limit the energy–momentum tensor becomes holomorphic equaling the Hawking flux of the four- and three-dimensional black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamic and statistical quantities for the non-local effective action approach.

UV/IR mode mixing and the CMB

It is well understood that spatial noncommutativity, if indeed realized in nature, is a phenomenon whose effects are not just felt at energy scales comparable to the noncommutativity scale. Loop effects can transmit signatures of any underlying noncommutativity to macroscopic scales (a manifestation of a phenomenon that has come to be known as UV/IR mode mixing) and offer a potential lever to constrain the amount of noncommutativity present in nature, if present at all. Field theories defined on noncommutative spaces (realized in string theory when D-branes are coupled to backgrounds of nontrivial RR background flux), can exhibit strong UV/IR mode mixing, manifesting in a nonlocal one-loop effective action. In the context of inflation in the presence of any background noncommutativity, we demonstrate how this UV/IR mixing at the loop level can allow us to place severe constraints on the scale of noncommutativity if we presume inflation is responsible for large-scale structure. We demonstrate that any amount of noncommutativity greatly suppresses the cosmic microwave background power at all observable scales, independent of the scale of inflation, and independent of whether or not the noncommutativity tensor redshifts during inflation, therefore nullifying a very salient and successful prediction of inflation.

The AdS/CFT/unparticle correspondence

We examine the correspondence between the anti-de Sitter (AdS) description of conformal field theories (CFTs) and the unparticle description of CFTs. We show how unparticle actions are equivalent to holographic boundary actions for fields in AdS, and how massive unparticles provide a new type of infrared cutoff that can be simply implemented in AdS by a soft breaking of conformal symmetry. We also show that processes involving scalar unparticles with dimensions ds < 2 or fermion unparticles with dimensionsdf < 5/2 are insensitive to ultraviolet cutoff effects. Finally we show that gauge interactions for unparticles can be described by bulk gauge interactions in AdS and that they correspond to minimal gauging of the non-local effective action, and we compute the fermion unparticle production cross-section.

Casimir energies with finite-width mirrors

We use a functional approach to the Casimir effect in order to evaluate the exact vacuum energy for a real scalar field in $d+1$ dimensions, in the presence of backgrounds that, in a particular limit, impose Dirichlet boundary conditions on one or two parallel surfaces. Outside of that limit, the backgrounds are described by a nonlocal effective action and may be thought of as modelling finite-width mirrors with frequency-dependent transmission and reflection coefficients. We obtain formal expressions for the Casimir energy in general backgrounds, and provide new explicit results in some particular cases.

QCD condensates with flavor SU(3) symmetry breaking from the instanton vacuum

Abstract We investigate the effects of flavor SU(3)-symmetry breaking on the quark, gluon, and mixed quark–gluon condensates, based on the nonlocal effective chiral action from the instanton vacuum. We take into account the effects of the flavor SU(3) symmetry breaking in the effective chiral action, so that the dynamical quark mass depends on the current quark mass ( m f ) . We compare the results of the present approach with those without the current quark mass dependence of the dynamical quark mass. It is found that the result of the quark condensate is decreased by about 30% as m f increases to 200 MeV, while that of the quark–gluon mixed condensates is diminished by about 15%. We obtain the ratios of the quark and quark–gluon mixed condensates, respectively: [ 〈 s ¯ s 〉 / 〈 u ¯ u 〉 ] 1 / 3 = 0.75 and [ 〈 s ¯ σ μ ν G μ ν s 〉 / 〈 u ¯ σ μ ν G μ ν u 〉 ] 1 / 5 = 0.87 . It turns out that the dimensional parameter m 0 2 = 〈 q ¯ σ μ ν G μ ν q 〉 / 〈 q ¯ q 〉 = 1.60 – 1.92 GeV 2 .

Fermion mass generation in de Sitter space

We study the one-loop radiative corrections for massless fermions in de Sitter space induced by a Yukawa coupling to a light, nearly minimally coupled scalar field. We show that the fermions acquire a mass. Next we construct the corresponding (nonlocal) effective fermionic action, which -- in contrast to the case of a massive Dirac fermion -- preserves chirality. Nevertheless, the resulting fermion dynamics is precisely that of a Dirac fermion with a mass proportional to the expansion rate. Our finding supports the view that an observer or a test particle responds to a scalar field in inflation by shifting its energy rather than seeing a thermal bath.

Infrared Asymptotics of the Heat Kernel and Nonlocal Effective Action

We review recent results in the nonperturbative theory of the heat kernel and its late-time asymptotic properties responsible for the infrared behavior of the quantum effective action for massless theories. In particular, we derive a generalization of the Coleman-Weinberg potential for theories with an inhomogeneous background field. This generalization represents a new nonlocal, nonperturbative action accounting for the effects in a transition domain between the space-time interior and its infinity. In four dimensions, these effects delocalize the logarithmic Coleman-Weinberg potential, while in d > 4, they are dominated by a new powerlike, renormalization-independent nonlocal structure. We also consider the nonperturbative behavior of the heat kernel in a curved space-time with an asymptotically flat geometry. In particular, we analyze the conformal properties of the heat kernel for a conformally invariant scalar field and discuss the problem of segregating the local cosmological term from the nonlocal effective action.

Nonlocal quantum gravity and the size of the universe

AbstractMotivated by the conjecture that the cosmological constant problem is solved by strong quantum effects in the infrared we use the exact flow equation of Quantum Einstein Gravity to determine the renormalization group behavior of a class of nonlocal effective actions. They consist of the Einstein‐Hilbert term and a general nonlinear function Fk(V) of the Euclidean spacetime volume V. For the V + V ln V‐invariant the renormalization group running enormously suppresses the value of the renormalized curvature which results from Planck‐size parameters specified at the Planck scale. One obtains very large, i.e., almost flat universes without finetuning the cosmological constant. A critical infrared fixed point is found where gravity is scale invariant.

Effective chiral Lagrangian in the chiral limit from the instanton vacuum

We study the effective chiral Lagrangian in the chiral limit from the instanton vacuum. Starting from the nonlocal effective chiral action, we derive the effective chiral Lagrangian, using the derivative expansion to order ${O(p}^{4})$ in the chiral limit. The low energy constants ${L}_{1},$ ${L}_{2},$ and ${L}_{3}$ are determined and compared with various models and the corresponding empirical data. The results are in a good agreement with the data. We also discuss the upper limit of the sigma meson, based on the present results.

SU(N) confining strings

String representations of the Wilson loop are constructed in the SU(N)-version of compact QED in three and four dimensions. This is done exactly in the case of the fundamental Wilson loop and in the large-N limit in the case of the adjoint Wilson loop. Using for concreteness the three-dimensional fundamental case, it is demonstrated how the resulting SU(N)-generalization of the so-called theory of confining strings can be obtained in various ways. In its weak-field limit (corresponding to the limit of low monopole densities), this theory enables one to fix the value of the string tension, which cannot be fixed when deduced from the mean magnetic field inside a flat contour (the derivation of this field is also presented). Moreover, the obtained theory enables one to find also the coupling constants of terms in the expansion of the nonlocal string effective action, which are higher in the derivatives than the Nambu-Goto term (some of these terms vanish at the flat surface). In the four-dimensional case with the theta-term, the critical values of the theta-parameter, at which the problem of crumpling of large world sheets might be solved, are found in both the fundamental case and in the large-N limit of the adjoint case. These values are only accessible provided the electric coupling constant is larger than a certain value, in accordance with the known fact that confinement in the four-dimensional compact QED holds in the strong-coupling regime.

A class of nonlocal truncations in quantum Einstein gravity and its renormalization group behavior

Motivated by the conjecture that the cosmological constant problem could be solved by strong quantum effects in the infrared we use the exact flow equation of Quantum Einstein Gravity to determine the renormalization group behavior of a class of nonlocal effective actions. They consist of the Einstein-Hilbert term and a general nonlinear function F(k, V) of the Euclidean space-time volume V. A partial differential equation governing its dependence on the scale k is derived and its fixed point is analyzed. For the more restrictive truncation of theory space where F(k, V) is of the form V+V ln V, V+V^2, and V+\sqrt{V}, respectively, the renormalization group equations for the running couplings are solved numerically. The results are used in order to determine the k-dependent curvature of the S^4-type Euclidean space-times which are solutions to the effective Einstein equations, i.e. stationary points of the scale dependent effective action. For the V+V ln V-invariant (discussed earlier by Taylor and Veneziano) we find that the renormalization group running enormously suppresses the value of the renormalized curvature which results from Planck-size bare parameters specified at the Planck scale. Hence one can obtain very large, almost flat universes without fine-tuning the cosmological constant.

New nonlocal effective action

We suggest a new method for the calculation of the nonlocal part of the effective action. It is based on resummation of perturbation series for the heat kernel and its functional trace at large values of the proper time parameter. We derive a new, essentially nonperturbative, nonlocal contribution to the effective action in spacetimes with dimensions $d>2$.

Weyl cohomology and the effective action for conformal anomalies

We present a general method of deriving the effective action for conformal anomalies in any even dimension, which satisfies the Wess-Zumino consistency condition by construction. The method relies on defining the coboundary operator of the local Weyl group, and giving a cohomological interpretation to counterterms in the effective action in dimensional regularization with respect to this group. Non-trivial cocycles of the Weyl group arise from local functionals that are Weyl invariant in and only in the physical even integer dimension. In the physical dimension the non-trivial cocycles generate covariant non-local action functionals characterized by sensitivity to global Weyl rescalings. The non-local action so obtained is unique up to the addition of trivial cocycles and Weyl invariant terms, both of which are insensitive to global Weyl rescalings. These distinct behaviors under rigid dilations can be used to distinguish between infrared relevant and irrelevant operators in a generally covariant manner. Variation of the $d=4$ non-local effective action yields two new conserved geometric stress tensors with local traces. The method may be extended to any even dimension by making use of the general construction of conformal invariants given by Fefferman and Graham. As a corollary, conformal field theory behavior of correlators at the asymptotic infinity of either anti-de Sitter or de Sitter spacetimes follows, i.e. AdS$_{d+1}$ or deS$_{d+1}$/CFT$_d$ correspondence. The same construction naturally selects all infrared relevant terms (and only those terms) in the low energy effective action of gravity in any even integer dimension. The infrared relevant terms arising from the known anomalies in d=4 imply that the classical Einstein theory is modified at large distances.

Covariant perturbation theory and the Randall–Sundrum picture

The effective action for quantum fields on a d-dimensional spacetime can be computed using a non-local expansion in powers of the curvature. We show explicitly that, for conformal fields and up to quadratic order in the curvature, the non-local effective action is equivalent to the d+1 action for classical gravity in AdS d+1 restricted to a ( d−1)-brane. This generalizes previous results about quantum corrections to the Newtonian potential and provides an alternative method for making local a non-local effective action. The equivalence can be easily understood by comparing the Kallen–Lehmann decomposition of the classical propagator with the spectral representation of the non-local form factors in the quantum effective action.

Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence

We compute the conformal anomaly of free d=6 superconformal (2,0) tensor multiplet on generic curved background. Up to a trivial covariant total-derivative term, it is given by the sum of the type A part proportional to the 6-d Euler density, and the type B part containing three independent Weyl invariants. Multiplied by factor 4N^3, the type B part of the anomaly reproduces exactly the corresponding part of the conformal anomaly of large N multiple M5-brane (2,0) theory as predicted (hep-th/9806087) by the AdS/CFT correspondence. The coefficients of the type A anomaly differ by the factor 4/7 x 4 N^3, so that the free tensor multiplet anomaly does not vanish on a Ricci-flat background. The coefficient 4N^3 is the same as found (hep-th/9703040) in the comparison of the tensor multiplet theory and the d=11 supergravity results for the absorption cross-sections of gravitons by M5 branes, and in the comparison (hep-th/9911135) of 2- and 3-point stress tensor correlators of the free tensor multiplet with the AdS_7 supergravity predictions. The reason for this coincidence is that the three Weyl-invariant terms in the anomaly are related to the $h^2$ and $h^3$ terms in the near flat space expansion of the corresponding non-local effective action, and thus to the 2-point and 3-point stress tensor correlators in flat background. At the same time, the type A anomaly is related to the $h^4$ term in the non-local part of the effective action, i.e. to a certain structure in the 4-point correlation function of stress tensors.

Non-local low-energy effective action for gravity with torsion

In this work we calculate the low-energy effective action for gravity with torsion, obtained after the integration of scalar and fermionic matter fields, using the local momentum representation based on the Riemann normal coordinates expansion. By considering this expansion around different spacetime points, we also compute the non-local terms together with the more usual divergent ones. Finally, we discuss the applicability of our results to the calculation of particle production probabilities.