Remarks on brane and antibrane dynamics
Received: June
Remarks on brane and antibrane dynamics
Ben Michel 0 1 3
Eric Mintun 0 1 3
Joseph Polchinski 0 1 2
Andrea Puhm 0 1 3
Philip Saad 0 1 3
0 Santa Barbara , CA 93106-4030 , U.S.A
1 Santa Barbara , CA 93106 , U.S.A
2 Kavli Institute for Theoretical Physics, University of California
3 Department of Physics, University of California
We develop the point of view that brane actions should be understood in the context of effective field theory, and that this is the correct way to treat classical as well as loop divergences. We illustrate this idea in a simple model. We then consider the implications for the dynamics of antibranes in flux backgrounds, focusing on the simplest case of a single antibrane. We argue that that effective field theory gives a valid description of the antibrane, and that there is no instability in this approximation. Further, conservation laws exclude possible nonperturbative decays, aside from the well-known NS5-brane instanton.
D-branes; dS vacua in string theory; Superstring Vacua
1 Introduction
Effective brane actions
Antibranes in fluxes
Application of EFT
More on antibrane dynamics
Brane actions are important for understanding many aspects of string physics. However,
their precise interpretation is somewhat ambiguous. A brane is a source for the bulk fields,
which are singular at the brane itself. If these fields are then inserted into the brane action,
the result is divergent. Many applications use a probe approximation, in which the
selffields of a brane are not included in the brane’s action. This is like a formal limit in which
the number of branes goes to zero.
A more general approach is to interpret the brane action in the context of effective field
theory. Here, all effects are included, and divergences are treated via the usual framework
For brane actions, this has been developed in ref. [2], which shows that
renormalization is the appropriate tool even for classical divergences such as those described
above.1 This can even lead to renormalization group flows of the type usually associated
with quantum loops. In this paper we develop this point of view further, and show that it
is useful in resolving some vexing issues in the literature.
In section 2 we present a simple model that illustrates how the framework of ref. [1]
applies to branes.
We discuss the matching onto the UV theory in various cases. In
section 3 we apply the EFT point of view to anti-D-branes in a flux background, focusing
primarily on the case of a single antibrane.2
We recover the phenomenon [9, 10] that
in a flux background both branes and antibranes are screened by a background charge
of the opposite sign. Divergences of the screening cloud near the brane are resolved by
matching onto string theory at short distance and are not sources of instability. We show
that possible nonperturbative annihilation of the antibrane and polarization cloud, while
consistent with conservation of brane charge, is inconsistent with the H3 Bianchi identity.
1Related earlier work includes refs. [3–7].
2For a review of the extensive literature on the supergravity descriptions of antibranes in flux backgrounds
and a complete list of references see [8].
Further, the apparent impossibility of black branes with antibrane charge [11–13] is avoided
by proper account of a Bohm-Aharonov phase. The only allowed antibrane instability is
the NS5-brane instanton of ref. [14].
Effective brane actions
We illustrate the principle of effective brane actions with a simple model that captures the
classical divergence problem noted above, and which gives a nice illustration of the general
S = − 2
q6=n−1
r − 2 − 2q
for directions orthogonal to the brane. For given d and p there will be only a finite number
of renormalizable interactions, but in the spirit of effective field theory we keep all
interactions, with nonrenormalizable interactions suppressed by the appropriate power of a large
as string theory, in which these general interactions will be generated. If we are interested
This point of view also requires that we keep general interactions in the bulk, but
for simplicity we have omitted these. The form (2.1) is stable under renormalization. To
arbitrary derivatives. Again, this form is stable under renormalization.
plitude for k1 → k2 scattering in the presence of the brane is
function as indicated.
At second order, figure 1b, the amplitude is
for r ≥ 2. To analyze this, we cut the integral off at k
r − 2 − q
r = 2n + 1 ,
, r = 2n . (2.4)
(2) =
T =
2kk − g k
T =
This dominates the leading term (2.2) in the IR, as it should because the interaction is
relevant. Further graphs form a geometric series, beginning with figure 1c, giving in all
The interaction is attractive for positive g, consistent with the formation of a bound state.
For codimension r = 2, there is a log divergence,
Again we can sum the geometric series,
marginal. These logarithms and their RG interpretation were discussed in ref. [2]. In
that (...truncated)