Suitable Counterterms Research Articles

QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case

We use the two-flavor Linear Sigma Model with quarks to study the phase structure of isospin asymmetric matter at zero temperature. The meson degrees of freedom provide the mean field chiral and isospin condensates on top of which we compute the effective potential accounting for constituent quark fluctuations at one-loop order. Using the renormalizability of the model, we absorb the ultraviolet divergences into suitable counterterms that are added respecting the original structure of the theory. These counterterms are determined from the stability conditions which require the effective potential to have minima in the condensates directions at the classical values, as well as the transition from the noncondensed to the condensed phase to be smooth as a function of the isospin chemical potential. We use the model to study the evolution of the condensates as well as the pressure, energy and isospin densities and the sound velocity as functions of the isospin chemical potential. The approach does a good average description up to isospin chemical potentials values not too large as compared to the vacuum pion mass.

A general framework for gravitational charges and holographic renormalization

We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques. This framework encompasses both localized charges associated with space–time subregions, as well as global conserved charges of the full space–time. Expressions for the charges include contributions from the boundary and corner terms in the subregion action, and are rendered unambiguous by appealing to the variational principle for the subregion, which selects a preferred form of the symplectic flux through the boundaries. The Poisson brackets of the charges on the subregion phase space are shown to reproduce the bracket of Barnich and Troessaert for open subsystems, thereby giving a novel derivation of this bracket from first principles. In the context of asymptotic boundaries, we show that the procedure of holographic renormalization can be always applied to obtain finite charges and fluxes once suitable counterterms have been found to ensure a finite action. This enables the study of larger asymptotic symmetry groups by loosening the boundary conditions imposed at infinity. We further present an algorithm for explicitly computing the counterterms that renormalize the action and symplectic potential, and, as an application of our framework, demonstrate that it reproduces known expressions for the charges of the generalized Bondi–Metzner–Sachs algebra.

Numerical integration of loop integrals through local cancellation of threshold singularities

We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with suitable counterterms and the imaginary part is a sum of two-body phase space integrals, constituting a locally finite representation of the generalised optical theorem. These expressions are integrals in momentum space, whose integrands were specially designed to feature local cancellations of threshold singularities. Such a representation is well suited for Monte Carlo integration and avoids the drawbacks of a numerical contour deformation around remaining singularities. Our method is directly applicable to a range integrals with certain geometric properties but not yet fully generalised for arbitrary one-loop integrals. We demonstrate the computational performance with examples of one-loop integrals with various kinematic configurations, which gives promising prospects for an extension to multi-loop integrals.

Momentum mappings for subtractions at higher orders in QCD

Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the addition of suitable counterterms. Such counterterms may be defined using momentum mappings, which are parametrisations of the phase space that factorise the variables that describe the particles becoming unresolved in some infrared or collinear limit from the variables that describe an on-shell phase space for the resolved particles. In this work, we review existing momentum mappings in a unified framework and introduce new ones for final-collinear and soft counterterms. The new mappings work in the presence of massive particles and with an arbitrary number of soft particles or of clusters of collinear particles, making them fit for subtraction methods at any order in perturbation theory. The new mapping for final-collinear counterterms is also used to elucidate relations among existing final-collinear mappings.

Tree-level bispectrum in the effective field theory of large-scale structure extended to massive neutrinos

We compute the tree-level bispectrum of dark matter in the presence of massive neutrinos in the mildly non-linear regime in the context of the effective field theory of large-scale structure (EFTofLSS) . For neutrinos, whose typical free streaming wavenumber (kfs) is longer than the non-linear scale (kNL), we solve a Boltzmann equation coupled to the effective fluid equation for dark matter. We solve perturbatively the coupled system by expanding in powers of the neutrino density fraction (fν) and the ratio of the wavenumber of interest over the non-linear scale (k/kNL) and add suitable counterterms to remove the dependence from short distance physics. For equilateral configurations, we find that the total-matter tree-level bispectrum is approximately 16fν times the dark matter one on short scales (k > kfs). The largest contribution stems from the back-reaction of massive neutrinos on the dark matter growth factor. On large scales (k < kfs) the contribution of neutrinos to the bispectrum is smaller by up to two orders of magnitude.

Non-perturbatively gauge-fixed compact U(1) lattice gauge theory

An extensive study of the compact U(1) lattice gauge theory with a higher derivative gauge-fixing term and a suitable counter-term has been undertaken to determine the nature of the possible continuum limits for a wide range of the parameters, especially at strong gauge couplings (g > 1), adding to our previous study at a single gauge coupling g = 1.3 [1]. Our major conclusion is that a continuum limit of free massless photons(with the redundant pure gauge degrees of freedom decoupled) is achieved at any gauge coupling, not necessarily small, provided the coefficient tilde{kappa} of the gauge-fixing term is sufficiently large. In fact, the region of continuous phase transition leading to the above physics in the strong gauge coupling region is found to be analytically connected to the point g = 0 and tilde{kappa}to infty where the classical action has a global unique minimum, around which weak coupling perturbation theory in bare parameters is defined, controlling the physics of the whole region. A second major conclusion is that, local algorithms like Multihit Metropolis fail to produce faithful field configurations with large values of the coefficient tilde{kappa} of the higher derivative gauge-fixing term and at large lattice volumes. A global algorithm like Hybrid Monte Carlo, although at times slow to move out of metastabilities, generally is able to produce faithful configurations and has been used extensively in the current study.

Charged rotating dilaton black strings with logarithmic nonlinear source

We find a new class of charged rotating dilaton black string solutions in the presence of logarithmic nonlinear electrodynamics. The dilaton potential is chosen in the form of the Liouville-type. We also present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. We find the conserved and thermodynamic quantities and check that the first law of thermodynamics holds on the black string horizon. We also address some theoretical implications of the nonlinear black hole/string solutions.

Thermodynamics of rotating black branes in higher dimensional Einstein – nonlinear electrodynamics – dilaton gravity

In this paper, we propose a n-dimensional action in which gravity is coupled to exponential nonlinear electrodynamics and scalar dilaton field with Liouville-type potential. By varying the action, we obtain the field equations. Then, we construct a new class of charged, rotating black brane solutions, with k = [(n – 1)/2] rotation parameters, of this theory. Because of the presence of the Liouville-type dilaton potential, the asymptotic behavior of the obtained solutions is neither flat nor (anti)-de Sitter. We investigate the causal structure of the space–time in ample details. We find the suitable counter term that removes the divergences of the action in the presence of the dilaton field, and calculate the conserved and thermodynamic quantities of the space–time. Interestingly enough, we find that the conserved quantities crucially depend on the dilaton coupling constant, α, while they are independent of the nonlinear parameter, β. We also check the validity of the first law of thermodynamics on the black brane horizon. Finally, we study thermal stability of the solutions by computing the heat capacity in the canonical ensemble. We disclose the effects of rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions.

Rotating black branes inf(R)gravity coupled to nonlinear Maxwell field

A class of higher dimensional rotating solutions in $R+f(R)$ theory coupled to a conformally invariant Maxwell field is presented. These solutions have asymptotically anti--de Sitter behavior but exist only for dimensions which are multiples of four. These solutions represent black branes with cylindrical or toroidal horizons and $k$ rotation parameters. We present the suitable counterterm which removes the divergences of the action in $R+f(R)$ gravity with constant curvature. We also compute the mass, the angular momenta, the entropy, the charge, and the electric potential of the black branes. Finally, we check that the conserved and thermodynamic quantities satisfy the first law of thermodynamics.

Supersymmetry Breaking in a Minimal Anomalous Extension of the MSSM

We study a supersymmetry breaking mechanism in the context of a minimal anomalous extension of the MSSM. The anomaly cancellation mechanism is achieved through suitable counterterms in the effective action, that is, the Green-Schwarz terms. We assume that the standard MSSM superpotential is perturbatively realized; that is, all terms allowed by gauge symmetries except for the μ-term which has a nonperturbative origin. The presence of this term is expected in many intersecting D-brane models which can be considered as the ultraviolet completion of our model. We show how soft supersymmetry breaking terms arise in this framework, and we study the effect of some phenomenological constraints on this scenario.

Magnetic strings in f(R) gravity

We construct a new class of spinning magnetic string solutions in f(R) gravity with constant scalar curvature. These solutions which produce a longitudinal magnetic field have no curvature singularity and no horizon, but have a conic geometry with a deficit angle. We also generalize this class of solutions to the case of spinning magnetic solutions with one rotation parameter. We find that the spinning string has a net electric charge which is proportional to the rotation parameter. With choosing a suitable counterterm, we remove the divergences of the action. The conserved quantities of the solutions are also calculated by using the counterterm method.

Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity

Hairy black holes and gravitational solitons in three dimensions for the new (BHT) massive gravity theory are considered at the special case when there is a unique maximally symmetric solution. Following the Brown-York approach with suitable counterterms, it is shown that the soliton possesses a fixed negative mass which coincides with that of AdS spacetime regardless the value of the integration constant that describes it. The soliton is then regarded as a degenerate ground state labeled by a modulus parameter. The Euclidean action is shown to be finite and independent of modulus and hair parameters for both classes of solutions, reproducing the hairy black hole free energy. Modular invariance implies that the gravitational hair becomes determined by the modulus parameter. Cardy formula is shown to agree with the semiclassical entropy provided the modulus parameter of the ground state is spontaneously fixed, suggesting that the hairy black hole is in a broken phase. Indeed, it is found that the critical temperature T c = (2πl)−1 characterizes a first order phase transition between the static hairy black hole and the soliton which, due to the existence of gravitational hair, can take place in the semiclassical regime.

Renormalization of minimally doubled fermions

We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Borici-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Borici-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.

Quantum field theory on the degenerate Moyal space

We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangian. Despite the apparent simplicity of the model, it raises several non-trivial questions. Our result is a first step towards the definition of renormalisable quantum field theories on a non-commutative Minkowski space.

Charged rotating dilaton black branes in AdS universe

We present the metric for the $(n+1)$-dimensional charged rotating dilaton black branes with cylindrical or toroidal horizons in the background of anti-de Sitter spacetime. We find the suitable counterterm which removes the divergences of the action in the presence of the dilaton potential in all higher dimensions. We plot the Penrose diagrams of the spacetime and reveal that the spacetime geometry crucially modifies in the presence of the dilaton field. The conserved and thermodynamic quantities of the black branes are also computed.

Magnetic dilaton strings in anti-de Sitter spaces

With an appropriate combination of three Liouville-type dilaton potentials, we construct a new class of spinning magnetic dilaton string solutions which produces a longitudinal magnetic field in the background of anti-de Sitter spacetime. These solutions have no curvature singularity and no horizon, but have a conic geometry. We find that the spinning string has a net electric charge which is proportional to the rotation parameter. We present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. We also calculate the conserved quantities of the solutions by using the counterterm method.

Use of a convenient size-extensive normalization in multi-reference coupled cluster (MRCC) theory with incomplete model space: A novel valence universal MRCC formulation

We present in this paper a size-extensive formulation of a valence universal multi-reference coupled cluster (VU-MRCC) theory which uses a general incomplete model space (IMS). The earlier formulations by Mukherjee [D. Mukherjee, Chem. Phys. Lett. 125 (1986) 207] led to size-extensive Heff which was both connected and ‘closed’, thereby leading to size-extensive energies. However, this necessitated abandoning the intermediate normalization (IN) for the valence universal wave-operator Ω when represented as a normal ordered exponential cluster Ansatz Ω≡{exp(S)} with S as the cluster operator. The lack of IN stemmed from the excitation operator Sq-op which leads to excitations into the complementary model space by their action on at least one model function. The powers of Sq-op can in general bring a model function ϕi back to another model function ϕj, and this is the reason why Ω does not respect IN. Sq-op are all labelled by active orbitals only. To achieve connectivity of Heff, it must be a ‘closed’ operator. A closed operator is one which always produces a model function by its action on another model function. Since the decoupling conditions Lq-op=0, and Lop=0 for the transformed operator L=Ω-1HΩ would be in conflict with Ωq-op=1q-op, the model space projection of Ω, PΩP=P cannot be maintained for the normal ordered Ansatz. This leads to a somewhat awkward expression for Heff. Bera et al. [N. Bera, S. Ghosh, D. Mukherjee, S. Chattopadhyay, J. Phys. Chem. A 109 (2005) 11462] recently tried to simplify the expression for Heff, and accomplished this by introducing suitable counter-terms Xcl in Ω to enforce Ωcl=1cl. We show in this paper that Heff in this formulation leads to a disconnected Heff, though it is equivalent by a similarity transformation to a connected effective hamiltonian H∼eff. Guided by the insight gleaned from this demonstration, we have proposed in this paper a new form of the wave-operator which never generates any powers of Sq-op, which is closed. This ‘externally projected’ wave-operator does not need counter-terms Xcl and automatically ensures Ωcl=1cl, thereby yielding directly a closed connected H∼eff. The desirable features of the traditional normal ordered Ansatz, such as the valence universality, subsystem embedding conditions hierarchical decoupling of the VU-MRCC equations for decreasing valence ranks are all satisfied by this new Ansatz for the wave-operator.

Charged rotating dilaton black strings in (A)dS spaces

We derive a class of charged rotating dilaton black string solutions in the background of anti-de Sitter spaces with an appropriate combination of three Liouville-type dilaton potentials. We also present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. The solutions are analyzed and their thermodynamics are discussed by using the counterterm method.

Electroweak symmetry breaking and radion stabilization in universal extra dimensions

We discuss the stabilization of the scalar sector, including the radion, in the gauge model with one universal extra dimension, within Higgs and Higgsless scenarios. The stabilization occurs at the one-loop level, through the fermionic contribution to the effective potential; in the Higgs case, for stabilization to take place the bosonic contribution must be balanced by the fermionic one, hence the scales of these two cannot differ too much. However, there is no need for (softly broken) supersymmetry to achieve the stabilization - it can be arranged for a reasonably wide range of couplings and mass scales. The primary instability in the model is the run-away of the radion vacuum expectation value. It turns out that the requirement of the radion stability, in the Higgs case, favours a Higgs boson mass below 0.26 TeV, which is consistent with the Standard Model upper bound that follows from the electroweak precision measurements. The typical radion mass is of the order of 10^{-6} eV. The radion mass can be made larger by rising the scale of fermion masses, as clearly seen in the Higgsless case. The cosmological constant may be cancelled by suitable counterterms, in such a way that the stabilization is not affected.

Succesful renormalization of a QCD-inspired Hamiltonian

The long standing problem of non perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. The approach provides new physical insight into nature of gauge theory and the potential energy of QCD and QED near the origin. The so obtained formalism is applied to physical mesons with a different flavor of quark and anti-quark. The excitation spectrum of the $\rho$-meson with its excellent agreement between theory and experiment is discussed as a pedagogical example.