Non-perturbative Instanton Effects Research Articles

Remark on the Dunne-Ünsal relation in exact semiclassics

Recently, it is realized that non-perturbative instanton effects can be generated to all orders by perturbation theory around a degenerate minima via Dunne-Unsal relation in several quantum mechanical systems. In this work we verify the Dunne-Unsal relation for resonance energy levels of one-dimensional polynomial anharmonic oscillators. We show that the relation is applicable to cubic and quartic anharmonic oscillators which are genus one potentials. However for higher order (higher genus) anharmonic potentials the relation is not satisfied and is subject to a certain extension.

Instanton effects in orbifold ABJM theory

We study the partition function of the orbifold ABJM theory on $S^3$, which is the $\mathcal{N}=4$ necklace quiver Chern-Simons-matter theory with alternating levels, in the Fermi gas formalism. We find that the grand potential of the orbifold ABJM theory is expressed explicitly in terms of that of the ABJM theory. As shown previously, the ABJM grand potential consists of the naive but primary non-oscillatory term and the subsidiary infinitely-replicated oscillatory terms. We find that the subsidiary oscillatory terms of the ABJM theory actually give a non-oscillatory primary term of the orbifold ABJM theory. Also, interestingly, the perturbative part in the ABJM theory results in a novel instanton contribution in the orbifold theory. We also present a physical interpretation for the non-perturbative instanton effects.

Open string amplitudes and large order behavior in topological string theory

We propose a formalism inspired by matrix models to compute open and closed topological string amplitudes in the B-model on toric Calabi-Yau manifolds. We find closed expressions for various open string amplitudes beyond the disk, and in particular we write down the annulus amplitude in terms of theta functions on a Riemann surface. We test these ideas on local curves and local surfaces, providing in this way generating functionals for open Gromov-Witten invariants in the spirit of mirror symmetry. In the case of local curves, we study the open string sector near the critical point which leads to 2d gravity, and we show that toric D-branes become FZZT branes in a double-scaling limit. We use this connection to compute non-perturbative instanton effects due to D-branes that control the large order behavior of topological string theory on these backgrounds.

Neutrino Majorana masses from string theory instanton effects

Finding a plausible origin for right-handed neutrino Majorana masses in semirealistic compactifications of string theory remains one of the most difficult problems in string phenomenology. We argue that right-handed neutrino Majorana masses are induced by non-perturbative instanton effects in certain classes of string compactifications in which the $U(1)_{B-L}$ gauge boson has a St\"uckelberg mass. The induced operators are of the form $e^{-U}\nu_R\nu_R$ where $U$ is a closed string modulus whose imaginary part transforms appropriately under $B-L$. This mass term may be quite large since this is not a gauge instanton and $Re U$ is not directly related to SM gauge couplings. Thus the size of the induced right-handed neutrino masses could be a few orders of magnitude below the string scale, as phenomenologically required. It is also argued that this origin for neutrino masses would predict the existence of R-parity in SUSY versions of the SM. Finally we comment on other phenomenological applications of similar instanton effects, like the generation of a $\mu$-term, or of Yukawa couplings forbidden in perturbation theory.

Mass generation for an ultralight axion

If a global chiral symmetry is explicitly broken by anomalies in nonabelian gauge theories, a pseudo Nambu-Goldstone boson (axion) associated with a spontaneous breakdown of such a global symmetry acquires a mass through nonperturbative instanton effects. We calculate the axion mass assuming a supersymmetric SU(2) gauge theory and show that the axion obtains an extremely small mass when the SU(2) gauge symmetry is broken down at very high energy, say at the Planck scale. We identify the axion with a hypothetical ultralight boson field proposed to account for a small but nonzero cosmological constant suggested from recent cosmological observations.

Effective action for membrane dynamics in DLCQ M theory on a two-torus

The effective action for the membrane dynamics on the background geometry of the $N$-sector DLCQ $M$ theory compactified on a two-torus is computed via supergravity. We compare it to the effective action obtained from the matrix theory, i.e., the (2+1)-dimensional supersymmetric Yang-Mills (SYM) theory, including the one-loop perturbative and full non-perturbative instanton effects. Consistent with the DLCQ prescription of $M$ theory {\em a la} Susskind, we find the precise agreement for the finite $N$-sector (off-conformal regime), as well as for the large $N$ limit (conformal regime), providing us with a concrete example of the correspondence between the matrix theory and the DLCQ $M$ theory. Non-perturbative instanton effects in the SYM theory conspire to yield the eleven-dimensionally covariant effective action.

Non-perturbative decoupling of heavy fermions

We show that heavy fermions decouple from the low energy physics also in non-perturbative instanton effects. Provided the heavy fermions are lighter than the symmetry breaking scale, all the instanton effects should be expressed as local operators in the effective Lagrangian. The effective theory itself doesn't admit instantons. We present the mechanism which suppresses instantons in the effective theory.

Spin-dependent forces and electromagnetic structure of the nucleon.

The spin-dependent forces, which can arise from either nonperturbative instanton effects or perturbative color magnetic interactions, cause the difference between u-quark and d-quark spatial distributions inside the nucleon. Considering this SU(6) symmetry-breaking effect, the elastic electromagnetic nucleon form factors and static magnetic moments of octet baryons can be well reproduced in the center-of-mass (c.m.) bag model. The same spin force effects on the deep inelastic polarized structure functions are also discussed.

Weak interactions are weak at high energies

We use a Schrödinger picture version of the instanton calculus to analyze the suggestion that nonperturbative instanton effects, such as baryon number violation in the electroweak interaction, can become large in high-energy scattering. We confirm that the euclidean instanton results of Ringwald, Espinosa and others are correct, for models with instantons of definite size, at low energy, and present a physical explanation of the energy dependence of amplitudes found by these authors. However, we show that their dilute instanton gas approximation breaks down at higher energy. Our techniques permit us to extend the energy regine in which a reliable calculation can be done. We find that the basic e 1/α suppression of the total cross section for instanton-induced processes persists at all energies, even ∼ M/α.

Nonperturbative effects on factorization in high-momentum processes

It is pointed out that the usual demonstrations within QCD perturbation theory of factorization at high-momentum transfers are incomplete when nonperturbative instanton effects are incorporated in a dilute gas approximation. The apparent violation of factorization does not vanish at large Q 2.