Standard Field Theory Techniques Research Articles

Chern-Simons-Higgs model as a theory of protein molecules

In this paper, we discuss a one-dimensional Abelian-Higgs model with Chern-Simons interaction as an effective theory of one-dimensional curves embedded in a three-dimensional space. We demonstrate how this effective model is compatible with the geometry of protein molecules. Using standard field theory techniques, we analyze phenomenologically interesting static configurations of the model and discuss their stability. This simple model predicts some characteristic relations for the geometry of secondary structure motifs of proteins, and we show how this is consistent with the experimental data. After using the data to universally fix basic local geometric parameters, such as the curvature and torsion of the helical motifs, we are left with a single free parameter. We explain how this parameter controls the abundance and shape of the principal motifs (alpha helices, beta strands, and loops connecting them).

A de Sitter Farey tail

We consider quantum Einstein gravity in three dimensional de Sitter space. The Euclidean path integral is formulated as a sum over geometries, including both perturbative loop corrections and nonperturbative instanton corrections coming from geometries with nontrivial topology. These nontrivial geometries have a natural physical interpretation. Conventional wisdom states that the sphere is the unique Euclidean continuation of de Sitter space. However, when considering physics only in the causal patch of a single observer other Euclidean geometries, in this case lens spaces, contribute to physical observables. This induces quantum gravitational effects which lead to deviations from the standard thermal behavior obtained by analytic continuation from the three sphere. The sum over these geometries can be formulated as a sum over cosets of the modular group; this is the de Sitter analog of the celebrated ``black hole Farey Tail.'' We compute the vacuum partition function including the sum over these geometries. Perturbative quantum corrections are computed to all orders in perturbation theory using the relationship between Einstein gravity and Chern-Simons theory, which is checked explicitly at tree and one-loop level using heat kernel techniques. The vacuum partition function, including all instanton and perturbative corrections, is shown to diverge in a way which cannot be regulated using standard field theory techniques.

Notes on wall crossing and instanton in compactified gauge theory with matter

We study the quantum effects on the Coulomb branch of N=2 SU(2) supersymmetric Yang-Mills with fundamental matters compactified on R^3 x S^1, and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.

Exact superpotentials for theories with flavors via a matrix integral

We extend and test the method of Dijkgraaf and Vafa for computing the superpotential of $\mathcal{N}=1$ theories to include flavors in the fundamental representation of the gauge group. This amounts to computing the contribution to the superpotential from surfaces with one boundary in the matrix integral. We compute exactly the effective superpotential for the case of the gauge group ${U(N}_{c}),$ ${N}_{f}$ massive flavor chiral multiplets in the fundamental and one massive chiral multiplet in the adjoint, together with a Yukawa coupling. We compare up to sixth order with the result obtained by standard field theory techniques in the already nontrivial case of ${N}_{c}=2$ and ${N}_{f}=1.$ The agreement is perfect.

Instanton effects in three-dimensional supersymmetric gauge theories with matter

Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that the asymptotic metric on the Coulomb branch coincides with the metric on Dancer's deformation of the monopole moduli space. For the N=2 theory with $N_f$ flavors, we compute the one-loop corrections to the metric and complex structure on the Coulomb branch. We then determine the superpotential including one-loop effects around the instanton background. These calculations provide an explicit check of several results previously obtained by symmetry and holomorphy arguments.

Remarks on the static potential in quantum chromodynamics

We derive the Wilson loop formula for the static quark-antiquark potential using standard field-theory techniques. We also discuss the limitations of a static potential as a description of higher-order effects.