Higgs phases at non-zero density from holography

Abstract

We show how Higgs phases at non-zero density can be described using a simple analytic method for gauge theories possessing a holographic dual. We introduce co-dimension one branes in a bottom-up gravity dual that are sources of form flux, such that the effective curvature radius is changed when the brane is crossed. This mimics the expected flow produced by color branes nucleating in a top-down model.

The weak gravity conjecture, overcharged shells and gravitational traps

“…The second critical point at ∂ R W = 0 is a local minimum since the potential V → 0 as R → ∞. 10 Note that if we assume that the shell can go (or start) from infinity R → ∞, we get for negative w, − 1 2 ⩽ w < 0. Note that for this range of w, the potential in equation (3.64) is bounded at R → ∞ as expected.…”

“…To study overcharged shells, we should consider the case of a negative w < 0 since as we have seen above, when w ⩾ 0 (p ⩾ 0) the shell is always undercharged 10 . Taking a derivative of equation ( 3.62) we find the equation of motion of the shell…”

“…The cosmic censorship for overcharged shells has also been discussed in [8]. Overcharged brane shells have also been exploited in [9] from compactifications of type IIB string theory and from holographic perspective in [10], whereas, the stability of spherical shells of matter in Newtonian gravity and general relativity has been discussed in [11][12][13][14][15][16][17][18]. Thereby, extended stable objects satisfying the WGC and consistent with the cosmic censorship exist already in classical Einstein-Maxwell theory.…”