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June 6, 2007

Tunnelling branes

It’s well-known that, in certain respects, low-energy brane dynamics can differ markedly from naïve field theory expectations. An important example is D-brane inflation, where the DBI action allows much steeper potentials to be compatible with inflation.

There’s a very interesting recent paper which argues that the DBI action, similarly, modifies the Coleman-de Luccia tunnelling rate, governing the decay of the false vacuum by bubble nucleation. The main effect is that the DBI action modifies the domain wall tension

(1)T=dϕV 0(2fV 0) T = \int d\phi \sqrt{V_0(2-f V_0)}

where the potential has a true minimum, V(ϕ )=V V(\phi_-)=V_- and a local minimum, V(ϕ +)=V +V(\phi_+)=V_+. V 0(ϕ)=V(ϕ)+V +/f(ϕ) V_0(\phi) = V(\phi) + V_+/f(\phi) f(ϕ)f(\phi) is the warp factor, which appears in the Euclidean DBI action as S E=2π 2ρ 3dρ(1f(ϕ)1+f(ϕ)ϕ˙ 21f(ϕ)+V(ϕ)) S_E = 2\pi^2 \int \rho^3 d\rho \left(\frac{1}{f(\phi)} \sqrt{1+f(\phi) \dot{\phi}^2}- \frac{1}{f(\phi)} +V(\phi)\right) Dot represents derivative with respect to ρ\rho and we’ve taken an O(4)O(4) symmetric ansatz. In the absence of warping, f(ϕ)=α 2f(\phi)={\alpha'}^2. In the limit f0f\to 0, we recover the usual thin-wall formula. But as V 0f2V_0 f\to 2, the tension can be much smaller than expected.

In the absence of gravity, the decay rate per unit volume Γ/Ve π 2Tρ¯ 3/2=e 27π 2T 4/2ϵ 3 \Gamma/V \sim e^{- \pi^2 T \overline{\rho}^3/2} = e^{-27\pi^2 T^4/2\epsilon^3} where ϵ=V +V \epsilon = V_+-V_- and the radius of the bubble is ρ¯=3T/ϵ\overline{\rho}=3T/\epsilon. So (1) can have a huge effect on the lifetime of the false vacuum.

Gravitational corrections modify ρ¯\overline{\rho} ρ¯=3TM pϵ 2M p 2+3T 2(V ++V )/2 \overline{\rho} = \frac{3 T M_p}{\sqrt{\epsilon^2 M_p^2 +3 T^2 (V_++V_-)/2}} and contribute an “extra” gravitational contribution in the exponent, just as is the usual case. But the qualitative effect remains: the lifetime of these metastable open string vacua can be *much* shorter than the naïve CDL result.

Posted by distler at June 6, 2007 12:31 PM

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