N = 1 supergravity BPS domain walls on Kähler–Ricci soliton

Abstract

This paper provides a study of some aspects of flat and curved BPS domain walls together with their Lorentz invariant vacua of four dimensional chiral N = 1 supergravity. The scalar manifold can be viewed as a one-parameter family of Kähler manifolds generated by a Kähler-Ricci flow equation. Consequently, a vacuum manifold characterized by (m, λ) where m and λ are the dimension and the index of the manifold, respectively, does deform with respect to the flow parameter related to the geometric soliton. Moreover, one has to carry out the renormalization group analysis to verify the existence of such a vacuum manifold in the ultraviolet or infrared regions. At the end, we discuss a simple model with linear superpotential on U(n) symmetric Kähler-Ricci orbifolds.

Curved Dyonic Domain Walls in Four Dimensions

“…If the electric and magnetic charges are included in the setup, then the domain walls interpolate two ground states of constant scalar curvature which are not Einstein. These generalize our previous results in neutral domain walls discussed [2][3][4][5][6] in which they connect two Einstein spaces, particularly anti-de Sitter spaces. This paper provides our preliminary results on curved dyonic domain walls of four dimensional Einstein-Maxwell-Higgs theory.…”

“…Since domain wall interpolates between ground states of different "cosmological" constant in the asymptotic limit, both cases are possible are possible. In the context of field theory the results in Theorem 1 describe an uncharged domain wall [2][3][4][5][6] .…”

“…Theorem 2 Suppose we have the condition (6) . Similar as in Theorem 1, the results in Theorem 2 describe a charged domain walls in the asymptotic regions interpolating between the spaces of constant scalar curvature which are not Einstein.…”

4d N = 1 Supersymmetric Yang-Mills Theories on Kahler-Ricci Soliton

“…For example, we have previous serial papers studying solitonic solutions of four dimensional N = 1 local supersymmetry (supergravity) on Kahler manifolds satisying Kahler-Ricci flow equation (Cao, 1985). Our results show that in the of both domain walls (Gunara and Zen, 2009a;Gunara et al, 2011) and black holes (Gunara, 2012) in general deform with respect to a flow parameter related to Kahler-Ricci equation. Moreover, this flow could change the nature of stability of domain walls and geometry of black holes.…”