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Register a new userNoncommutative Moduli for Multi-Instantons
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There exists a recursive algorithm for constructing BPST-type multi-instantons on commutative R^4. When deformed noncommutatively, however, it becomes difficult to write down non-singular instanton configurations with topological charge greater than one in explicit form. We circumvent this difficulty by allowing for the translational instanton moduli to become noncommutative as well. This makes possible the ADHM construction of t Hooft multi-instanton solutions with everywhere self-dual field strengths on noncommutative R^4.
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We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulae show that the instanton gas is ultra-dilute, due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their back-reaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painleve I equation.
Moduli with flat or run-away classical potentials are generic in theories based on supersymmetry and extra dimensions. They mix between themselves and with matter fields in kinetic terms and in the nonperturbative superpotentials. As the result, interesting structure appears in the scalar potential which helps to stabilise and trap moduli and leads to multi-field inflation. The new and attractive feature of multi-inflationary setup are isocurvature perturbations which can modify in an interesting way the final spectrum of primordial fluctuations resulting from inflation.
We analyze the mechanism of condensation of orientational moduli (as introduced in [25]) on multi-Skyrmionic configurations of the four-dimensional Skyrme model. The present analysis reveals interesting novel features. First of all, the orientational moduli tend to decrease the repulsive interactions between Skyrmions, the effect decreasing with the increase of the Baryon number. Moreover, in the case of a single Skyrmion, the appearance of moduli is energetically favorable if finite volume effects are present. Otherwise, in the usual flat topologically trivial case, it is not. In the low energy theory these solutions can be interpreted as Skyrmions with additional isospin degrees of freedom.
In this letter we argue that instanton-dominated Greens functions in N=2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version of the theory. Defining an appropriate BRST operator (as a supersymmetry plus a gauge variation), we also show that the expansion coefficients of the Seiberg-Witten effective action for the low-energy degrees of freedom can be written as integrals of total derivatives over the moduli space of self-dual gauge connections.
Based on the properties of probability distributions of functions of random variables, we proposed earlier a simple stringy mechanism that prefers the meta-stable vacua with a small cosmological constant Lambda. As an illustration of this approach, we study in this paper particularly simple but non-trivial models of the Kahler uplift in the large volume flux compactification scenario in Type IIB string theory, where all parameters introduced in the model are treated either as fixed constants motivated by physics, or as random variables with some given uniform probability distributions. We determine the value w_0 of the superpotential W_0 at the supersymmetric minima, and find that the resulting probability distribution P(w_0) peaks at w_0=0; furthermore, this peaking behavior strengthens as the number of complex structure moduli increases. The resulting probability distribution P(Lambda) for meta-stable vacua also peaks as Lambda -> 0, for both positive and negative Lambda. This peaking/divergent behavior of P(Lambda) strengthens as the number of moduli increases. In some scenarios for Lambda > 0, the likely value of Lambda decreases exponentially as the number of moduli increases. The light cosmological moduli issue accompanying a very small Lambda is also mentioned.
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