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P. H. Damgaard

Publications and source records attributed to P. H. Damgaard.

At least 37 records · Page 2Linked to original sources
arXiv2006

Extracting $F_π$ from small lattices: unquenched results

We calculate the response of the microscopic Dirac spectrum to an imaginary isospin chemical potential for QCD with two dynamical flavors in the chiral limit. This extends our previous calculation from the quenched to the unquenched theory. The resulting spectral correlation function in the $ε$-regime provides here, too, a new and efficient way to measure $F_π$ on the lattice. We test the method in a hybrid Monte Carlo simulation of the theory with two staggered quarks.

hep-lat↗
arXiv2005

A New Method for Determining $F_π$ on the Lattice

We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $ε$-regime of QCD. This correlation function has a unique and strong dependence on $F_π$, and thus provides an novel way to extract $F_π$ from lattice simulations. We test the method in a quenched lattice simulation with staggered fermions.

hep-lat↗
arXiv2004

The Replica Method and Toda Lattice Equations for QCD_3

We consider the epsilon-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in the number of flavors. Taking the replica limit of these Toda equations allows us to derive the microscopic spectral correlation functions for the QCD Dirac operator in 3 dimensions. For an even number of flavors we reproduce known results derived using other techniques. In the case of an odd number of flavors the theory has a severe sign problem, and we obtain previously unknown microscopic spectral correlation functions.

hep-th↗
arXiv2004

Distributions of Dirac Operator Eigenvalues

The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions which are stated. As a special case, we give examples of the lowest-lying eigenvalue distributions for QCD-like gauge theories without making use of earlier results based on the relation to Random Matrix Theory.

hep-th↗
arXiv2003

Hamiltonian N=2 Superfield Quantization

We present a superfield construction of Hamiltonian quantization with N=2 supersymmetry generated by two fermionic charges Q^a. As a byproduct of the analysis we also derive a classically localized path integral from two fermionic objects Σ^a that can be viewed as ``square roots'' of the classical bosonic action under the product of a functional Poisson bracket.

hep-th↗
arXiv2003

Quenched and Unquenched Chiral Perturbation Theory in the ε-Regime

The chiral limit of finite-volume QCD is the $ε$-regime of the theory. We discuss how this regime can be used for determining low-energy observables of QCD by means of comparisons between lattice simulations and quenched and unquenched chiral perturbation theory. The quenched theory suffers in the $ε$-regime from ``quenched finite volume logs'', the finite-volume analogs of quenched chiral logs.

hep-lat↗
arXiv2003

Vector and Axial-Vector Propagators in the ε-Regime of QCD

Using quenched and unquenched chiral perturbation theory we compute vector and axial current two-point functions at finite volume and fixed gauge field topology, in the so-called ε-regime of QCD. A comparison of these results with finite volume lattice calculations allows to determine the parameters of the corresponding chiral Lagrangians.

hep-lat↗
arXiv2003

Finite-Size Scaling of Vector and Axial Current Correlators

Using quenched chiral perturbation theory, we compute the long-distance behaviour of two-point functions of flavour non-singlet axial and vector currents in a finite volume, for small quark masses, and at a fixed gauge-field topology. We also present the corresponding predictions for the unquenched theory at fixed topology. These results can in principle be used to measure the low-energy constants of the chiral Lagrangian, from lattice simulations in volumes much smaller than one pion Compton wavelength. We show that quenching has a dramatic effect on the vector correlator, which is argued to vanish to all orders, while the axial correlator appears to be a robust observable only moderately sensitive to quenching.

hep-lat↗
arXiv2002

Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories

It has been conjectured that spontaneous chiral symmetry breaking in strongly coupled vectorlike gauge theories falls into only three different classes, depending on the gauge group and the representations carried by the fermions. We test this proposal by studying SU(2), SU(3) and SU(4) lattice gauge theories with staggered fermions in different irreducible representations. Staggered fermions away from the continuum limit should, for all complex representations, still belong to the continuum class of spontaneous symmetry breaking. But for all real and pseudo-real representations we show that staggered fermions should belong to incorrect symmetry breaking classes away from the continuum, thus generalizing previous results. As an unambiguous signal for whether chiral symmetry breaks, and which breaking pattern it follows, we look at the smallest Dirac eigenvalue distributions. We find that the patterns of symmetry breaking are precisely those conjectured.

hep-lat↗
arXiv2002

Finite-size Scaling of Meson Propagators

Using quenched chiral perturbation theory we compute meson correlation functions at finite volume and fixed gauge field topology. We also present the corresponding analytical predictions for the unquenched theory at fixed gauge field topology. These results can be used to measure the low-energy parameters of the chiral Langrangian from lattice simulations in volumes much smaller than one pion Compton wavelength.

hep-lat↗
arXiv2001

The Microscopic Dirac Operator Spectrum

We review the exact results for microscopic Dirac operator spectra based on either Random Matrix Theory, or, equivalently, chiral Lagrangians. Implications for lattice calculations are discussed.

hep-lat↗
arXiv2001

Wilson Loops in ${\cal N}=4$ Supersymmetric Yang-Mills Theory from Random Matrix Theory

Based on the AdS/CFT correspondence, string theory has given exact predictions for circular Wilson loops in U(N) ${\cal N}=4$ supersymmetric Yang-Mills theory to all orders in a 1/N expansion. These Wilson loops can also be derived from Random Matrix Theory. In this paper we show that the result is generically insensitive to details of the Random Matrix Theory potential. We also compute all higher $k$-point correlation functions, which are needed for the evaluation of Wilson loops in arbitrary irreducible representations of U(N).

hep-th↗
arXiv2001

Quenched Finite Volume Logarithms

Quenched chiral perturbation theory is used to compute the first finite volume correction to the chiral condensate. The correction diverges logarithmically with the four-volume $V$. We point out that with dynamical quarks one can obtain both the chiral condensate and the pion decay constant from the distributions of the lowest Dirac operator eigenvalues.

hep-lat↗
arXiv2001

The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories

We confront Cardy's suggested c-function for four-dimensional field theories with the spontaneous breaking of chiral symmetries in asymptotically free vectorlike gauge theories with fermions transforming according to different representations under the gauge group. Assuming that the infrared limit of the c-function is determined by the dimension of the associated Goldstone manifold, we find that this c-function always decreases between the ultraviolet and infrared fixed points.

hep-th↗
arXiv2001

QCD3 and the Replica Method

Using the replica method, we analyze the mass dependence of the QCD3 partition function in a parameter range where the leading contribution is from the zero momentum Goldstone fields. Three complementary approaches are considered in this article. First, we derive exact relations between the QCD3 partition function and the QCD4 partition function continued to half-integer topological charge. The replica limit of these formulas results in exact relations between the corresponding microscopic spectral densities of QCD3 and QCD4. Replica calculations, which are exact for QCD4 at half-integer topological charge, thus result in exact expressions for the microscopic spectral density of the QCD3 Dirac operator. Second, we derive Virasoro constraints for the QCD3 partition function. They uniquely determine the small-mass expansion of the partition function and the corresponding sum rules for inverse Dirac eigenvalues. Due to de Wit-'t Hooft poles, the replica limit only reproduces the small mass expansion of the resolvent up to a finite number of terms. Third, the large mass expansion of the resolvent is obtained from the replica limit of a loop expansion of the QCD3 partition function. Because of Duistermaat-Heckman localization exact results are obtained for the microscopic spectral density in this way.

hep-th↗
arXiv2000

Spectral Sum Rules of the Dirac operator and Partially Quenched Chiral Condensates

Exploiting Virasoro constraints on the effective finite-volume partition function, we derive generalized Leutwyler-Smilga spectral sum rules of the Dirac operator to high order. By introducing $N_v$ fermion species of equal masses, we next use the Virasoro constraints to compute two (low-mass and large-mass) expansions of the partially quenched chiral condensate through the replica method of letting $N_v \to 0$. The low-mass expansion can only be pushed to a certain finite order due to de Wit-'t Hooft poles, but the large-mass expansion can be carried through to arbitrarily high order. Results agree exactly with earlier results obtained through both Random Matrix Theory and the supersymmetric method.

hep-th↗