Supersymmetry anomalies and some aspects of renormalization

We show how the $\text{L}$-matrix elements avoid the problem of supersymmetry breaking by the gauge fixing and ghost terms for renormalization in the Wess-Zumino gauge. Possible origins of supersymmetry anomalies are discussed. Gauge and gravitational anomalies induce a supersymmetry anomaly which has two distinct terms, one of which is gauge invariant. We give the expression for the noninvariant term for 2n-dimensional spacetime and for the invariant part in four dimensions. This anomaly, although cohomologically nontrivial, is still consistent with result that in superspace no supersymmetry anomaly is generated.     

Chiral anomaly in a spherical spacetime

We evaluate the chiral anomaly for a gauge theory on Sⁿ in the hyperspherical O(n + 1) covariant formalism using the method of Fujikawa and comment on related aspects.     

Global existence of coupled Yang-Mills and scalar fields in 2 + 1 dimensional space-time

We present results on the Cauchy problem for coupled classical Yang-Mills and scalar fields in n + 1 dimensional space-time both in the temporal and in the Lorentz gauge. We prove the existence of local solutions for any n, and the existence of global solutions for n = 1, 2 in the temporal gauge and for n = 1 in the Lorentz gauge. The last result also holds for massive Yang-Mill fields.     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

Anomaly cancelling terms from the elliptic genus

We calculate the heterotic string one-loop diagram in 2n + 2 dimensions with one external B_μν and n external gravitons and/or gauge bosons. The result is a modular integral over the weight zero terms of the character valued partition function (or elliptic genus) of the theory, and can be directly expressed in terms of the factor which multiplies TrF² − TrR² in the field theory anomaly. The integrands have a non-trivial dependence on the modular parameter τ, reflecting contributions not only from the physical massless states but also from an infinity of “unphysical” modes. Some of them are identical to integrands which have been discussed recently in relation with Atkin-Lehner symmetry and the cosmological constant. As a corollary we find a method to compute these integrals without using Atkin-Lehner transformations.     

Remark on the consistent gauge anomaly in supersymmetric theories

We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly d^abc=trT^a{T^b,T^c}, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinković as the solution of the Wess–Zumino consistency condition.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

Multicritical behavior of the two-field Ginzburg-Landau model coupled to a gauge field

In this paper, we study the multicritical behavior of the Ginzburg-Landau model in a O(n₁)⊕O(n₂)-symmetric version containing (n₁/2+n₂/2)-complex order parameters coupled to a gauge field. We develop the RG analysis at a one-loop approximation in the context of the ?-expansion approach. The beta functions are obtained, and in the case of equal couplings between the two scalar fields and the gauge field and n₁=n₂=n/2, the infrared stability of the fixed points is discussed. It is found that the charged infrared-stable fixed point exists for n>393.2. Calculations of the relevant critical exponents are also carried out.     

The β-function in supersymmetric Yang-Mills theory

We show by means of the Adler-Bardeen theorem how to calculate the two-loop β function from a one-loop calculation of the superconformal anomaly in a supersymmetric gauge theory with arbitrary superpotential. The N = 2 and N = 4 cases are also briefly discussed.     

Dimensional regularization of gauge theories in spherical spacetime: Free field trace anomalies

The O(n + 1) covariant formulation of massless quantum electrodynamics in spherical spacetime is further developed to allow a calculation of the energy-momentum tensor trace anomalies for the free Dirac, electromagnetic, and SU(2) gauge fields. The principal technical development is the construction of the Faddeev-Popov ghosts for electrodynamics and SU(2) Yang-Mills theory. This construction is unconventional first in that the gauge fixing term in the Lagrangian is not a perfect square, and second because it is necessary to remove radial as well as gauge degrees of freedom from the measure of the functional integral. The ghost fields are shown to satisfy a minimal scalar field equation. The free field effective action is found to be divergent in four dimensions, and is renormalized by the inclusion in the Lagrangian of a counterterm local in the gravitational fields. The energy-momentum tensor calculated from this renormalized effective action is shown to have a trace anomaly.     

An explicit example of a tumbling gauge theory

We present a class of two-dimensional models with a non-abelian gauge symmetry. In one model with gauge symmetry is dynamically broken by a fermion bilinear condensate in a $\text{1}\text{n}$ expansion. We discuss the differences between a dynamical and elementary Higgs mechanism due to the presence of a non-abelian axial anomaly.     

Relation between anomaly in type-I superstring and anomaly in its effective theory

We explicitly calculate the hexagon and heptagon (covariant) gauge anomaly including the precise numerical coefficients in type-I open superstring. The calculation is performed by using the Pauli-Villars regularization on the basis of the stringy Ward identity, which is an assumption weaker than the cancelled propagator argument. We show that the anomalies in the effective theory are realized as the zero slope limit (α^′→0) of the string anomalies in a very non-trivial way in the present calculational scheme. This non-trivial realization in higher point (n≧8) anomalies is also discussed.     

Contribution of the triangle graphs to the neutron electric dipole moment

In the Kobayashi-Maskawa model we compute a new contribution to the neutron electric dipole moment induced byCP violating flavour-changing transitions of the typess→d+gluon+γ through heavy quark loops. This contribution, essentially given by the triangle anomaly graph, is by itself gauge invariant. We obtain from this mechanismD _n /e=3.10^?32 cm, one order of magnitude below our previous estimate from usual penguin diagram contributions.     

An analytic calculation of the weak field limit of the static color dielectric constant

We analyze the Dyson equation/Ward identity system for the axial gauge n · A = 0 gluon propagator Δ_μν(q)whenn · q = 0. The solution behaves like (q^?4 + (q²)^ν?1) for small q₂, and we are able to calculate the power ν analytically. It turns out to be 0.1737. This analytic calculation verifies our earlier numerical solutions to these equations. For static problems, n · q = 0 is the temporal gauge, and in this gauge the gluon propagator is directly related to the color dielectric constant. We can thus calculate the dielectric constant in the infrared limit.     

N = 2 supersymmetric Yang-Mills theory and its supercurrent

Using the off-shell two-component formulation of N = 2 supersymmetric Yang-Mills theory and the gauge covariantized supersymmetry transformations for the fields, the non-abelian supercurrent and anomaly multiplets are developed and the transformation rules for their components are obtained. The superfields in N = 2 superspace whose components are the non-abelian supercurrent and anomaly multiplets are written down.     

Topological Geon Black Holes in Einstein-Yang-Mills Theory

We construct topological geon quotients of two families of Einstein-Yang-Mills black holes. For Künzle??s static, spherically symmetric SU(n) black holes with n?>?2, a geon quotient exists but generically requires promoting charge conjugation into a gauge symmetry. For Kleihaus and Kunz??s static, axially symmetric SU(2) black holes a geon quotient exists without gauging charge conjugation, and the parity of the gauge field winding number determines whether the geon gauge bundle is trivial. The geon??s gauge bundle structure is expected to have an imprint in the Hawking-Unruh effect for quantum fields that couple to the background gauge field.     

Compactification of Einstein-Yang-Mills theories on CPn

We study compactification of Einstein-Yang-Mills theories in 2n + 4 dimensions on the manifold CP_n, with a classical gauge field that is equal to the spin connection. The complete boson fluctuation spectrum is calculated and no tachyons, ghosts or massless scalars are found for the minimal Yang-Mills group SU(n) × U(1). For larger groups, tachyons or massless scalars may appear.     

Membrabe models and generalized Z2 gauge theories

We consider models of (d?n)-dimensional membranes fluctuating in a d-dimensional space under the action of surface tension. We investigate the renormalization properties of these models perturbatively and in $\text{1}\text{n}$ expansion. The potential relationships of these models to generalized Z₂ gauge theories are indicated.     

Abelian and non-Abelian anomalies in monopole-fermion interactions

Taking an example of the standard SU(5) theory, the monopole-fermion system is reduced to an effective 2-dimensional model. This is a generalized Schwinger model containing four Abelian gauge fields interacting with N generations of massless fermions through vector and axialvector couplings. We quantize such a system exactly in the canonical operator formalism. Then, analyzing the cluster property of operators carrying various chiral charges, the roles of the Abelian and non-Abelian anomalies are studied in monopole-induced baryon decay. We demonstrate that the Abelian anomaly and the charge-mixing boundary condition are the driving forces for monopole-induced baryon decay, though the conservation law suggests the importance of the non-Abelian anomaly.