Effective Action In Terms Research Articles

Finiteness of N=4 Super-Yang–Mills Effective Action in Terms of Dressed N=1 Superfields

We argue in favor of the independence on any scale, ultraviolet or infrared, in kernels of the effective action expressed in terms of dressed N=1 superfields for the case of N=4 super-Yang–Mills theory. Under “scale independence” of the effective action of dressed mean superfields, we mean its “finiteness in the off-shell limit of removing all the regularizations”. This off-shell limit is scale independent because no scale remains inside these kernels after removing the regularizations. We use two types of regularization: regularization by dimensional reduction and regularization by higher derivatives in its supersymmetric form. Based on the Slavnov–Taylor identity, we show that dressed fields of matter and of vector multiplets can be introduced to express the effective action in terms of them. Kernels of the effective action expressed in terms of such dressed effective fields do not depend on the ultraviolet scale. In the case of dimensional reduction, by using the developed technique, we show how the problem of inconsistency of the dimensional reduction can be solved. Using Piguet and Sibold formalism, we indicate that the dependence on the infrared scale disappears off shell in both the regularizations.

The Veneziano amplitude in AdS5×S3 from an 8-dimensional effective action

We study four-point functions of arbitrary half-BPS operators in a 4-dimensional mathcal{N} = 2 SCFT with flavour group SO(8) at genus-zero and strong ’t Hooft coupling, corresponding — via AdS/CFT — to the (α′ expansion of the) Veneziano amplitude on an AdS5×S3 background. We adapt a procedure first proposed by Abl, Heslop and Lipstein in the context of AdS5×S5, and postulate the existence of an effective action in terms of an 8-dimensional scalar field valued in the adjoint of the flavour group. The various Kaluza-Klein correlators can then be computed by uplifting the standard AdS/CFT prescription to the full product geometry with AdS bulk-to-boundary propagators and Witten diagrams replaced by suitable AdS5×S3 versions. After elucidating the main features of the procedure, valid at all orders in α′, we show explicit results up to order α′5. The results provide further evidence of a novel relation between AdS×S and flat amplitudes — which made its first appearance in mathcal{N} = 4 SYM — that is perhaps the most natural extension of the well known flat-space limit proposed by Penedones to cases where AdS and S have the same radius.

Integrating out beyond tree level and relativistic superfluids

We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a ϕ4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) ϕ4. We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry.

S-wave pion-pion scattering lengths from nucleon-meson fluctuations

We present calculations of the $S$-wave isospin-zero and isospin-two pion-pion scattering lengths within a nucleon-meson model with parity doubling. Both scattering lengths are computed in various approximations, ranging from a mean-field (MF) calculation toward the inclusion of loop corrections by means of the functional renormalization group (FRG). The bosonic part of the investigated nucleon-meson model is formulated in terms of stereographic projections as a ``natural'' set of coordinates on the respective vacuum manifold. We thereby elucidate subtleties concerning the truncation of the effective action with respect to higher-derivative pion interactions and the ``successful'' computation of the scattering lengths. As the main result, we find simultaneous agreement for the isospin-zero and isospin-two scattering lengths with experimental data within the ${\mathrm{LPA}}^{\ensuremath{'}}$ truncation of the FRG, together with chiral-symmetry breaking (roughly) occurring at the characteristic scale of $4\ensuremath{\pi}{f}_{\ensuremath{\pi}}$. The isoscalar $\ensuremath{\sigma}$ mass is dynamically generated by the FRG integration of momentum modes and is a prediction of the model. It ends being of the order of 500 MeV, i.e., much lower than the value ($>1\text{ }\text{ }\mathrm{GeV}$) found in MF or one-loop treatment of this or related models. Finally, the convergence of the corresponding low-energy expansion of the quantum effective action in terms of pion momenta is discussed.

Fundamental scale invariance

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional renormalization flow equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling solution vanish. Realistic particle physics and quantum gravity are compatible with this setting. The non-linear restrictions for scaling solutions can explain properties as an asymptotically vanishing cosmological constant or dynamical dark energy that would seem to need fine tuning of parameters from a perturbative viewpoint. As an example we discuss a pregeometry based on a diffeomorphism invariant Yang-Mills theory. It is a candidate for an ultraviolet completion of quantum gravity with a well behaved graviton propagator at short distances.

Quantum corrected gravitational potential beyond monopole-monopole interactions

We investigate spin- and velocity-dependent contributions to the gravitational inter-particle potential. The methodology adopted here is based on the expansion of the effective action in terms of form factors encoding quantum corrections. Restricting ourselves to corrections up to the level of the graviton propagator, we compute, in terms of general form factors, the non-relativistic gravitational potential associated with the scattering of spin-0 and -1/2 particles. We discuss comparative aspects concerning different types of scattered particles and we also establish some comparisons with the case of electromagnetic potentials. Moreover, we apply our results to explicit examples of form factors based on non-perturbative approaches for quantum gravity. Finally, the cancellation of Newtonian singularity is analysed in the presence of terms beyond the monopole-monopole sector.

Paradojas del comportamiento proambiental de los estudiantes universitarios en diferentes disciplinas académicas

The objective of the present study was to establish the characteristics of the pro environmental behavior of Colombian university students; that is, to identify the attitudes, beliefs, valuations, practices and environmental knowledge of Colombian students from different university careers. For this purpose, a cross-sectional descriptive-correlational study was carried out with a sample of 1503 students from different university careers in five Colombian cities, with an incidence probability of .5, 95 % confidence and an error of 2.5 %. The participants were randomly selected within each university and the questionnaires applied were the Pro environmental Behaviour Inventory (ICP) and the Environmental Knowledge Test (TCA); the latter was developed specifically for the purposes of this research. The students surveyed were found to have positive environmental attitudes and beliefs in most dimensions. The level of environmental awareness of students in the five selected cities is low. Although no significant differences were observed between the careers with respect to beliefs, valuations, actions and environmental knowledge, paradoxically the students of environmental sciences occupied inferior places to those who study economic and administrative sciences. Thus, in the analysis of specific items it was evidenced that the students of environmental sciences develop diverse anti environmental actions, in a similar way to the behavior patterns of the students of the other researched careers. With respect to the region, the results show that it is possible to conclude that there are differences according to the city with respect to the beliefs, valuation, knowledge and environmental actions of the students surveyed. Among the findings it is worth highlighting the results of Bucaramanga in terms of the report of environmental actions and the highest average in the TCA observed in that city. Similarly, Cali stands out along with Bucaramanga in its results, while Medellin obtained the lowest scores in environmental knowledge. Finally, in the report on environmental actions in university students, contradictory results are observed, given that it presents a controversial profile because people perform pro-environmental and anti-environmental behaviors at the same time, with positive environmental attitudes and beliefs in accordance with these attitudes. Regarding the knowledge about the environment, in the descriptive results the average of the test was 12 points, which means that the students failed the test. The multivariate analysis showed that the theoretical model on which the construction of the ICP was based and the instruments from which items were selected for its conformation, apparently has great predictive power with respect to the verbal report of environmental actions; however, the TCA, a test constructed specifically for this research, would covariate with almost all the factors of the ICP but does not predict causally the actions reported by the students. In general, this study shows that university institutions and the Colombian government have the challenge of ensuring that environmental education achieves the expected results for the fulfillment of both the country and the world's environmental goals. The results also demonstrates the need to articulate policies, actions and regulations to improve the quality of environmental education in universities, as well as to implement citizen behavior programs that promote responsible consumption, given that knowledge does not correlate with effective actions in terms of public services, green brands and solid urban waste management, among other areas.

Sv-map between type I and heterotic sigma models

The scattering amplitudes of gauge bosons in heterotic and open superstring theories are related by the single-valued projection which yields heterotic amplitudes by selecting a subset of multiple zeta value coefficients in the α′ (string tension parameter) expansion of open string amplitudes. In the present work, we argue that this relation holds also at the level of low-energy expansions (or individual Feynman diagrams) of the respective effective actions, by investigating the beta functions of two-dimensional sigma models describing world-sheets of open and heterotic strings. We analyze the sigma model Feynman diagrams generating identical effective action terms in both theories and show that the heterotic coefficients are given by the single-valued projection of the open ones. The single-valued projection appears as a result of summing over all radial orderings of heterotic vertices on the complex plane representing string world-sheet.

Bosonic self-energy functional theory

We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean field theory when constraining to local fields, whereas when neglecting kinetic contributions of non-condensed bosons it reduces to the static mean-field approximation. To benchmark the theory we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase-boundaries, and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g. in the presence of non-trivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters, but nevertheless remain computable by modest means.

Noncommutative U(1) gauge theory from a worldline perspective

We study pure noncommutative U(1) gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance, and then employ the worldline formalism to write the one-loop effective action, singling out UV-divergent parts and finite (planar and non-planar) parts, and study renormalization properties of the theory. This amounts to employ worldline Feynman rules for the phase space path integral, that nicely incorporate the Fadeev-Popov ghost contribution and efficiently separate planar and non-planar contributions. We also show that the effective action calculation is independent of the choice of the worldline Green's function, that corresponds to a particular way of factoring out a particle zero-mode. This allows to employ homogeneous string-inspired Feynman rules that greatly simplify the computation.

Higher derivative terms in three dimensional supersymmetric theories

In this work, we systematically analyze higher derivative terms in the supersymmetric effective actions for three dimensional scalar field theories using $\mathcal{N} =1$ superspace formalism. In these effective actions, we show that auxiliary fields do not propagate and their effective actions can be expressed in terms of the physical fields. So, the theory does not change its field content upon addition of higher derivative terms. We use derivative expansion to generate four, five and six dimensional terms for an interacting scalar field theory with $\mathcal{N} =1$ supersymmetry. We show that along with pure fermionic and bosonic terms, there are various five and six dimensional topological terms that mix bosonic and fermionic fields. Finally, we use these results to obtain higher derivative topological terms in the effective action for two M2-branes.

Vacuum polarization corrections to low energy quark effective couplings

In this work corrections to low energy punctual effective quark couplings up to the eighth order are calculated by considering vacuum polarization effects with the scalar quark-antiquark condensate. The departing point is a QCD-based NJL model. By separating the quark field into two components, one that condenses and another one for interacting quarks, the former is integrated out with the help of usual auxiliary fields and an effective action in terms for interacting quark fields is found. The scalar auxiliary field reduces to the quark-antiquark condensate in the vacuum and the determinant is expanded in powers of the quark-antiquark bilinears generating chiral invariant effective 2N-quark interactions (N=2, 3...). The corresponding coupling constants and effective masses are estimated, and the general trend is that for increasing the effective gluon mass the values of the effective coupling constants decrease. All the values are in good agreement with phenomenological fits.

The renormalization of fluctuating branes, the Galileon and asymptotic safety

We consider the renormalization of d-dimensional hypersurfaces (branes) embedded in flat (d+1)-dimensional space. We parametrize the truncated effective action in terms of geometric invariants built from the extrinsic and intrinsic curvatures. We study the renormalization-group running of the couplings and explore the fixed-point structure. We find evidence for an ultraviolet fixed point similar to the one underlying the asymptotic-safety scenario of gravity. We also examine whether the structure of the Galileon theory, which can be reproduced in the nonrelativistic limit, is preserved at the quantum level.

On the interpretation of gravitational corrections to gauge couplings

Several recent papers discuss gravitational corrections to gauge couplings that depend quadratically on the energy. In the framework of the background-field approach, these correspond in general to adding to the effective action terms quadratic in the field strength but with higher-order space–time derivatives. We observe that such terms can be removed by appropriate local field redefinitions, and do not contribute to physical scattering-matrix elements. We illustrate this observation in the context of open string theory, where the effective action includes, among other terms, the well-known Born–Infeld form of non-linear electrodynamics. We conclude that the quadratically energy-dependent gravitational corrections are not physical in the sense of contributing to the running of a physically-measurable gauge coupling, or of unifying couplings as in string theory.

Permanent education in health in the supervised treatment of tuberculosis: a descriptive study

The study focuses on the contribution of permanent education (EP) in teaching Community Health Workers (ACS) about the supervised treatment of tuberculosis. This is a descriptive study with a qualitative approach, aiming to describe the difficulties faced by ACS in the supervised treatment of tuberculosis, and the facilities that are available to them. It aims to discuss the strategies adopted by ACS with regard to performing supervised treatment of tuberculosis. We also aim to propose effective actions in terms of permanent education for ACS with regard to the supervised treatment of tuberculosis. Data collection will be underaken through participant observation and semi-structured interviews with ten ACS of a family health unit in a municipality in the state of Rio de Janeiro, RJ. It is hoped that this study will contribute to the improvement of supervised treatment performed in the city, thus developing quality care and achieving a rate of reduction and the eventual elimination of cases of tuberculosis as recommended by the World Health Organization (WHO)

Generalized [formula omitted] topological amplitudes and holomorphic anomaly equation

In arXiv:0905.3629 we described a new class of N = 2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which appear at higher loops in heterotic string theory compactified on K 3 × T 2 . We analyze their effective field theory interpretation and derive particular (first order) differential equations as a consequence of supersymmetry Ward identities and the 1/2-BPS nature of the corresponding effective action terms. In string theory the latter get modified due to anomalous world-sheet boundary contributions, generalizing in a non-trivial way the familiar holomorphic and harmonicity anomalies studied in the past. We prove by direct computation that the subclass of topological amplitudes studied in arXiv:0905.3629 forms a closed set under these anomaly equations and that these equations are integrable.

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.

Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series

We derive three-dimensional, Z(N)-symmetric effective actions in terms of Polyakov loops by means of strong coupling expansions, starting from thermal SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in the literature, corresponding to the (spatial) strong coupling limit, is thus extended by several higher orders, as well as by additional interaction terms. We provide analytic mappings between the couplings of the effective theory and the parameters $N_\tau,\beta$ of the original thermal lattice theory, which can be systematically improved. We then investigate the deconfinement transition for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the effective theory. Our effective models correctly reproduce second order 3d Ising and first order phase transitions, respectively. Furthermore, we calculate the critical couplings $\beta_c(N_\tau)$ and find agreement with results from simulations of the 4d theory at the few percent level for $N_\tau=4-16$.

Effective Potential in the Strong-Coupling Lattice QCD with Next-to-Next-to-Leading Order Effects

We derive an analytic expression of the effective potential at finite temperature (T) and chemical potential (mu) in the strong-coupling lattice QCD for color SU(3) including next-to-next-to-leading order (NNLO) effects in the strong coupling expansion. NNLO effective action terms are systematically evaluated in the leading order of the large dimensional (1/d) expansion, and are found to come from some types of connected two plaquette configurations. We apply the extended Hubbard-Stratonovich transformation and a gluonic dressed fermion technique to the effective action, and obtain the effective potential as a function of T, mu, and two order parameters; chiral condensate and a vector potential field. The next-to-leading order (NLO) and NNLO effects result in modifications of the wave function renormalization factor, quark mass and chemical potential. We find that T_{c,mu=0} and mu_{c,T=0} are similar to the NLO results, whereas the position of the critical point is sensitive to NNLO corrections.

Nonequilibrium quantum criticality in bilayer itinerant ferromagnets

We present a theory of nonequilibrium quantum criticality in a coupled bilayer system of itinerant electron magnets. The model studied consists of the first layer subjected to an in-plane current and open to an external substrate. The second layer is subject to no direct external drive, but couples to the first layer via short-ranged spin-exchange interaction. No particle exchange is assumed between the layers. Starting from a microscopic fermionic model, we derive an effective action in terms of two coupled bosonic fields which are related to the magnetization fluctuations of the two layers. When there is no interlayer coupling, the two bosonic modes possess different dynamical critical exponents $z$ with $z=2$ $(z=3)$ for the first (second) layer. This results in multiscale quantum criticality in the coupled system. It is shown that the linear coupling between the two fields leads to a low-energy fixed point characterized by the larger dynamical critical exponent $z=3$. We compute the correlation length in the quantum disordered and quantum critical regimes for both the nonequilibrium case and in thermal equilibrium where the whole system is held at a common temperature $T$. We identify an effective temperature scale ${T}_{\text{eff}}$ with which we define a quantum-to-classical crossover that is in exact analogy with the thermal equilibrium case but with $T$ replaced by ${T}_{\text{eff}}$. However, we find that the leading correction to the correlation length in the quantum critical regime scales differently with respect to $T$ and ${T}_{\text{eff}}$. We also note that the current in the lower layer generates a drift of the magnetization fluctuations, manifesting itself as a parity-breaking contribution to the effective action of the bosonic modes. In this sense, the nonequilibrium drive in this system plays a role which is distinct from $T$ in the thermal equilibrium case. We also derive the stochastic dynamics obeyed by the critical fluctuations in the quantum critical regime and find that they do not fall into the previously identified dynamical universality classes.