Bare Coupling Research Articles

Ward identity determination of Z_{mathrm {S}}/Z_{mathrm {P}} for N_{mathrm {f}}=3 lattice QCD in a Schr\xf6dinger functional setup

We derive chiral Ward identities for lattice QCD with Wilson quarks and N_{mathrm{f}}ge 3 flavours, on small lattices with Schrödinger functional boundary conditions and vanishingly small quark masses. These identities relate the axial variation of the non-singlet pseudoscalar density to the scalar one, thus enabling the non-perturbative determination of the scale-independent ratio Z_{mathrm {S}}/Z_{mathrm {P}} of the renormalisation parameters of these operators. We obtain results for N_{mathrm{f}}=3 QCD with tree-level Symanzik-improved gluons and Wilson-Clover quarks, for bare gauge couplings which cover the typical range of large-volume N_{mathrm{f}}= 2+1 simulations with Wilson fermions at lattice spacings below 0.1,fm. The precision of our results varies from 0.3 to 1%, except for the coarsest lattice, where it is 2%. We discuss how the Z_{mathrm {S}}/Z_{mathrm {P}} ratio can be used in the non-perturbative calculations of {mathrm {O}}(a) improved renormalised quark masses.

NSVZ Relation and NSVZ Scheme in $$\mathcal{N} = 1$$ Non-Abelian Supersymmetric Gauge Theories

We briefly describe the perturbative derivation of the exact NSVZ $$\beta $$ -function for $$\mathcal{N} = 1$$ supersymmetric non-Abelian gauge theories in the case of using the higher covariant derivative regularization. It is demonstrated that with this regularization the NSVZ equation written in the form of a relation between the $$\beta $$ -function and the anomalous dimensions of the quantum superfields is satisfied by the renormalization group functions defined in terms of the bare couplings independently of a renormalization prescription. For the renormalization group functions defined in terms of the renormalized couplings this implies that one of the NSVZ schemes in all loops is given by the HD+MSL prescription, when the theory is regularized by higher derivatives and the renormalization constants contain only powers of $$ln\Lambda {\text{/}}\mu $$ . All these statements are verified by comparing certain terms in the three-loop $$\beta $$ -function with the corresponding contributions to anomalous dimensions of the quantum superfields.

Two-loop renormalization of the matter superfields and finiteness of mathcal{N} = 1 supersymmetric gauge theories regularized by higher derivatives

The two-loop anomalous dimension of the chiral matter superfields is calculated for a general mathcal{N} = 1 supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of the bare couplings, and the one defined in terms of the renormalized couplings for an arbitrary renormalization prescription. For the one-loop finite theories we find a simple relation between the higher derivative regulators under which the anomalous dimension defined in terms of the bare couplings vanishes in the considered approximation. In this case the one-loop finite theory is also two-loop finite in the HD+MSL scheme. Using the assumption that with the higher covariant derivative regularization the NSVZ equation is satisfied for RGFs defined in terms of the bare couplings, we construct the expression for the three-loop β-function. Again, the result is written both for the β-function defined in terms of the bare couplings and for the one defined in terms of the renormalized couplings for an arbitrary renormalization prescription.

New approach to lattice QCD at finite density; results for the critical end point on coarse lattices

All approaches currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test an algorithm, sign reweighting, that works directly at finite μ = μB /3 and is yet free from any such uncontrolled systematics. With this algorithm the only problem is the sign problem itself. This approach involves the generation of configurations with the positive fermionic weight |Re det D(μ)| where D(μ) is the Dirac matrix and the signs sign(Re det D(μ)) = ±1 are handled by a discrete reweighting. Hence there are only two sectors, +1 and −1 and as long as the average 〈±1〉 ≠ 0 (with respect to the positive weight) this discrete reweighting by the signs carries no overlap problem and the results are reliable. The approach is tested on Nt = 4 lattices with 2 + 1 flavors and physical quark masses using the unimproved staggered discretization. By measuring the Fisher (sometimes also called Lee-Yang) zeros in the bare coupling on spatial lattices L/a = 8, 10, 12 we conclude that the cross-over present at μ = 0 becomes stronger at μ > 0 and is consistent with a true phase transition at around μB /T ∼ 2.4.

Three-loop verification of a new algorithm for the calculation of a β-function in supersymmetric theories regularized by higher derivatives for the case of [formula omitted] SQED

We verify a recently proposed method for obtaining a β-function of N=1 supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a β-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagrams. The result is produced in the form of a certain integral of double total derivatives with respect to the loop momenta. Here we compare the results obtained for the three-loop β-function of N=1 SQED in the general ξ-gauge with the help of this method and with the help of the standard calculation. Their coincidence confirms the correctness of the new method and the general argumentation used for its derivation. Also we verify that in the considered approximation the NSVZ relation is valid for the renormalization group functions defined in terms of the bare coupling constant and for the ones defined in terms of the renormalized coupling constant in the HD+MSL scheme, both its sides being gauge-independent.

Attractive polaron formed in doped nonchiral/chiral parabolic system within ladder approximation

We investigate the properties of attractive polaron formed by a single impurity dressed with the particle-hole excitations in a three-dimensional (3D) doped (extrinsic) parabolic system. Base on the single particle-hole variational ansatz, we study the pair propagator, self-energy, and the non-self-consistent medium T-matrix. The non-self-consistent T-matrix discussed in this paper contains only the open channel since we do not consider the shift of center-of-mass due to the resonance (e.g., induced by the magnetic field). The scattering form factor is discussed in detail for the chiral case and compared to the non-chiral one. The effects of the bare coupling strength, which is momentum-cutoff-dependent, are also discussed. We found that the pair propagator and the related quantities, like the self-energy, spectral function, induced effective mass, and residue (spectral weight), all exhibit some novel features in the low-momentum regime which are different from the high one. That also related to the polaronic instabilities as well as the many-body fluctuation and nonadiabatic/adiabatic dynamics. The effects of chirality and the finite-temperature (much lower than the critical one) are studied in detail, and our results can also be used in exploring other weak-coupling systems with mobile impurity.

Exact \u03b2-function of Yang-Mills theory in 2+1 dimensions

To set the stage, I discuss the β-function of the massless O(N) model in three dimensions, which can be calculated exactly in the large N limit. Then, I consider SU(N) Yang-Mills theory in 2+1 space-time dimensions. Relating the β-function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, Is how that frac{dln {g}^2/mu }{dln mu }=-1 for all g and all N in one particular renormalization scheme. As a consequence, I find that the Yang-Mills β-function in three dimensions must have the same sign for all finite and positive bare coupling parameters in any renormalization scheme, and all non-trivial infrared fixed points are unreachable in practice.

New dual representation for staggered lattice QCD

We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling $\beta= 2N/g^{2}$. Our method makes use of the recently developed formalism to evaluate the ${\rm SU}(N)$ $1-$link integrals and consists in an exact rewriting of the partition function in terms of a set of additional dual degrees of freedom which we call "Decoupling Operator Indices" (DOI). The method is not limited to any particular number of dimensions or gauge group ${\rm U}(N)$, ${\rm SU}(N)$. In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Worm-like algorithms. Higher order $\beta$-corrections to strong coupling lattice QCD can be, in principle, systematically evaluated, helping to answer the question whether the finite density sign problem remains mild when plaquette contributions are included. Issues related to the complexity of the description and strategies for the stochastic evaluation of the partition function are discussed.

The NSVZ \u03b2-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

The contributions of the matter superfields and of the Faddeev-Popov ghosts to the β-function of mathcal{N} = 1 supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the β-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the β-function beyond the one-loop approximation is given by the sum of the singular contributions, which is calculated in all orders for singularities produced by the matter superfields and by the Faddeev-Popov ghosts. The result is expressed in terms of the anomalous dimensions of these superfields. It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices.

Scaling theory of magnetism in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering and quantum-disordered state being investigated. The calculations taking into account magnon and incoherent spin dynamics are performed. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach. Possibility of a non-Fermi-liquid behavior is treated.

The NSVZ relation and the NSVZ scheme for N = 1 non-Abelian supersymmetric theories, regularized by higher covariant derivatives

We discuss, how the exact NSVZ -function appears in N = 1 supersymmetric non-Abelian gauge theories, regularized by higher covariant derivatives. In particular, we demonstrate that the renormalization group functions defined in terms of the bare couplings satisfy the NSVZ relation in the case of using this regularization. This occurs, because the loop integrals giving the -function are integrals of double total derivatives with respect to loop momenta. It is also shown that for the renormalization group functions standardly defined in terms of the renormalized couplings the NSVZ scheme can be obtained if the theory is regularized by higher covariant derivatives and only powers of ln/µ are included into the renormalization constants. These statements are confirmed by the explicit calculations in the three-loop approximation, where the scheme dependence is essential.

On the scaling theory of antiferromagnetic ordering in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering being investigated. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach.

The \u03b2-function of mathcal{N} = 1 supersymmetric gauge theories regularized by higher covariant derivatives as an integral of double total derivatives

For a general mathcal{N} = 1 supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the β-function defined in terms of the bare couplings is given by integrals of double total derivatives with respect to loop momenta. With the help of the technique used for this proof it is possible to construct a method for obtaining these loop integrals, which essentially simplifies the calculations. As an illustration of this method, we find the expression for the three-loop contribution to the β-function containing the Yukawa couplings and compare it with the result of the standard calculations made earlier. Also we briefly discuss, how the structure of the loop integrals for the β-function considered in this paper can be used for the all-loop perturbative derivation of the NSVZ relation in the non-Abelian case.

O(4) ϕ4 model as an effective light meson theory: A lattice-continuum comparison

We investigate the possibility of using the 4 dimensional $O(4)$ symmetric $\phi^4$ model as an effective theory for the sigma-pion system. We carry out lattice Monte Carlo simulations to establish the triviality bound in the case of explicitly broken symmetry and to compare it with results from continuum functional methods. In case of a physical parametrization we find that triviality restricts the possible lattice spacings to a narrow range, therefore cutoff independence in the effective theory sense is practically impossible for thermal quantities. We match the critical line in the space of bare couplings in the different approaches and compare vacuum physical quantities along the line of constant physics (LCP).

Three-loop contribution of the Faddeev\u2013Popov ghosts to the beta -function of mathcal{N}=1 supersymmetric gauge theories and the NSVZ relation

We find the three-loop contribution to the beta -function of mathcal{N}=1 supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev–Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the beta -function is compared with the two-loop anomalous dimension of the Faddeev–Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the beta -function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed.

Femtosecond laser written diamond waveguide excitation of the whispering gallery modes in a silicon microsphere

We demonstrate light coupling from femtosecond laser written diamond waveguide operating at the telecommunication wavelengths to a silicon microsphere resonator. Type II waveguides are written on a diamond platform and Fabry-Pérot resonances are excited in the diamond waveguides by bare fiber coupling in and out of the waveguide. The Fabry-Pérot resonances have a free spectral range of 87 pm, and a maximum Q-factor of 3.9 × 104. The diamond waveguide is used to excite TM-polarized whispering gallery modes of the 1 mm silicon microsphere, since the type II waveguides support TM modes better as compared to TE modes. The whispering gallery mode spacing is measured as 0.257 nm and the highest Q-factor is 6.2 × 104. This evanescent coupling method to high Q-factor silicon microsphere resonances by femtosecond laser written diamond waveguides can be further used for filtering and sensing applications in various photonic lightwave circuits.

Renormalization of the 4PI effective action using the functional renormalization group

Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of integral equations that must be solved truncates at the level of the action, and no additional approximations are needed. The main problem with the method is renormalization, which until now could only be done at the lowest ($n$=2) level. In this paper we show how to obtain renormalized results from an $n$-particle irreducible effective action at any order. We consider a symmetric scalar theory with quartic coupling in four dimensions and show that the 4 loop 4-particle-irreducible calculation can be renormalized using a renormalization group method. The calculation involves one bare mass and one bare coupling constant which are introduced at the level of the Lagrangian, and cannot be done using any known method by introducing counterterms.

On Dimensional Regularization in the Yang–Mills Theory

We suggest an asymptotic approach to renormalization in the case of dimensional regularization. As an example, the quantum Yang–Mills theory in the four-dimensional space-time is considered. A formula for the renormalized effective action is derived by using the asymptotic behavior of the bare coupling constant. Then we discuss the dimensional transmutation, the process of renormalization, and the properties of the coupling constant.

The three-loop Adler D-function for mathcal{N}=1 SQCD regularized by dimensional reduction

The three-loop Adler D-function for mathcal{N}=1 SQCD in the overline{mathrm{DR}} scheme is calculated starting from the three-loop result recently obtained with the higher covariant derivative regularization. For this purpose, for the theory regularized by higher derivatives we find a subtraction scheme in which the Green functions coincide with the ones obtained with the dimensional reduction and the modified minimal subtraction prescription for the renormalization of the SQCD coupling constant and of the matter superfields. Also we calculate the D-function in the overline{mathrm{DR}} scheme for all renormalization constants (including the one for the electromagnetic coupling constant which appears due to the SQCD corrections). It is shown that the results do not satisfy the NSVZ-like equation relating the D-function to the anomalous dimension of the matter superfields. However, the NSVZ-like scheme can be constructed with the help of a properly tuned finite renormalization. It is also demonstrated that the three-loop D-function defined in terms of the bare couplings with the dimensional reduction does not satisfy the NSVZ-like equation for an arbitrary renormalization prescription. We also investigate a possibility to present the results in the form of the β-expansion and the scheme dependence of this expansion.

Local manipulation of quantum magnetism in one-dimensional ultracold Fermi gases across narrow resonances

Effective range is a quantity to characterize the energy dependence in two-body scattering strength, and is widely used in cold atomic systems especially across narrow resonances. Here we show that the effective range can significantly modify the magnetic property of one-dimensional (1D) spin-$1/2$ fermions in the strongly repulsive regime. In particular, the effective range breaks the large spin degeneracy in the hard-core limit, and induces a Heisenberg exchange term in the spin chain that is much more sensitive to the local density than that induced by the bare coupling. With an external harmonic trap, this leads to a very rich magnetic pattern where the anti-ferromagnetic (AFM) and ferromagnetic (FM) correlations can coexist and distribute in highly tunable regions across the trap. Finally, we propose to detect the range-induced magnetic order in the tunneling experiment. Our results can be directly tested in 1D Fermi gases across narrow resonance, and suggest a convenient route towards the local manipulation of quantum magnetism in cold atoms.