Transcript PowerPoint Presentation

Supersymmetry and Gauge
Symmetry Breaking from
Intersecting Branes
A. Giveon, D.K.
hep-th/0703135
Introduction
One way to break supersymmetry in string
theory is to start with a supersymmetric
background, and add to it a collection of Dbranes that does not leave any unbroken
supercharges.
The dynamics of such backgrounds is in
general a non-trivial problem, which in some
cases can be addressed using existing
techniques.
Examples:
 Non-BPS D-branes and brane-antibrane
systems in flat spacetime.
 D-branes propagating in the vicinity of NS
fivebranes.
 Branes and antibranes wrapping cycles of
Calabi-Yau manifolds.
 D-brane models of chiral symmetry breaking.
In this talk we will discuss a system of this type,
which is related to some of the above examples
and to recent work on supersymmetry breaking
in field theory.
Our main emphasis will be on the classical
dynamics of the branes, but we will also
comment on quantum corrections.
The fivebrane configuration
We start with a supersymmetric configuration
which contains two types of NS5-branes
intersecting in 3+1 dimensions:
NS:
NS’:
(012345)
(012389)
They are placed as follows:
where we used the notation:
One can think of this configuration as a dual
description of a non-compact CY manifold.
For k=1 (one NS brane), each of the NS-NS’
intersections is dual to a conifold. y1, y2
correspond to resolution parameters of the two
conifolds; x2- x1 is the separation between them.
Thus, our discussion is relevant for the study of
non-supersymmetric brane systems on CalabiYau manifolds.
Adding D4-branes
To break supersymmetry, we add D4-branes
(shown in red) as follows:
We would like to analyze the low energy
dynamics of the branes as a function of the
parameters of the brane configuration, xi , yi , k.
The standard rules give a Yang-Mills theory with
gauge group
and fermions in the adjoint representation,
whose dynamics is described by N=1 SYM.
Supersymmetry is broken due to the presence of
a bifundamental scalar field corresponding to a
fundamental string stretched between the two
stacks of branes.
For large separation (x2- x1>>ls) it is massive, so
one might think that it can be ignored at low
energies, but we will see later that this is not
always the case.
More generally, we will see that while for small
fields the low energy dynamics is
supersymmetric, in some regions in parameter
space it is important to take into account large
field effects when analyzing these systems.
This is clear already at the simplest level of
discussion, where the fivebranes are treated as
hypersurfaces on which the D-branes can end.
Indeed, the brane configuration we started with
can be continuously deformed to:
The gauge symmetry is broken by the
reconnection of the branes:
To determine which of the two configurations is
the true ground state we need to compare their
energies. In the flat space approximation the
difference of energies is given by
This is positive for
and negative otherwise.
A couple of useful things to note:
 Both brane configurations break supersymmetry;
nevertheless, we will argue later that the vacuum
is in fact supersymmetric.
 Both configurations are classically locally stable
in this approximation. Thus the one with higher
energy can only decay by tunneling. We will see
that this expectation is modified when certain
classical corrections to our picture are included.
DBI analysis
The corrections in question are due to the effect
of the gravitational potential of the k NS-branes
on the D4-branes. It can be studied by analyzing
the dynamics of the D-branes in the geometry
created by the fivebranes.
The latter is given by the CHS geometry
with
The D-branes are described by the DBI action in
this background. This description is accurate at
large k, but is known to capture some features of
the dynamics exactly for small k as well.
We are looking for a solution in which the Dbranes are described by a smooth curve y=y(x),
connecting the point (x1,y1) and (x2,y2) . Its shape
is obtained by extremizing the DBI action
The solution takes the qualitative form
Its features depend on the values of the
parameters of the brane configuration. We next
describe its properties for y1=y2=y.
In this case, the parameters of the brane
configuration above are related as follows:
There are two distinct regimes: y<l and y>l.
For y<l, the smooth curved solution above only
exists for
and when it exists its energy
is lower than that of the straight brane solution
with unbroken gauge symmetry. In this regime,
the qualitative behavior of the potential for the
D4-branes is
The fact that the straight, unbroken brane
configuration is a local maximum of the potential
can also be understood by thinking about the
dynamics of a fundamental string stretched
between the branes and antibranes. Its lowest
mode is the open string tachyon, whose mass in
the linear dilaton throat of the fivebranes is
To summarize, for y<l the system undergoes a
second order phase transition at
. The
order parameter can be taken to be the vacuum
expectation value of the bifundamental tachyon
T, which behaves like
The energetics of the branes can be described by
the following plot:
For y>l one can repeat the above analysis, and
find the following energetics:
In this case the phase transition is first order:
Quantum effects
So far we discussed the dynamics of the branes
classically. It turns out that quantum effects lead
to interesting modifications. To see that, let’s go
back to our original brane configuration and
consider it for small x2-x1. In this regime the
brane configuration is a small deformation of:
This configuration corresponds to a gauge
theory with gauge group
and matter in the following representations:
There are bifundamentals of the gauge group,
and an adjoint of U(N2), with the superpotential
The second term is absent in the configuration of
the previous slide. It measures the separation of
the NS’-branes in the x direction,
The gauge theory description is good for small
separation. In that regime one can use it to
analyze the vacuum structure. Using standard
techniques, one finds that supersymmetry is
classically broken, but is restored quantum
mechanically. The classical, nonsupersymmetric, vacuum becomes a long-lived
excited state.
From the perspective of the brane system, this
means that the phase diagram contains another
line near the origin.
It is an interesting question what happens for
separations of order ls and larger. We believe
that these lines continue to this regime and the
vacuum is supersymmetric, but have not proven
that. Indeed, it would be surprising if the
supersymmetric ground states found in the field
theory analysis ceased to exist for finite x2-x1.
Also, the brane configurations we have been
studying are expected to be related by a stringy
version of Seiberg duality to
Comments
 We see that the ground states we found using
the classical DBI analysis are, likely, metastable,
with a lifetime that goes to infinity as the string
coupling goes to zero.
 In some region in parameter space our problem
reduces to the one studied in gauge theory by
ISS. In other regions one finds a stringy
generalization of their system, which exhibits
very similar qualitative phenomena.
 Much remains to be done to sort out the detailed
dynamics of this system. For example, it would
be nice to prove directly in string theory that a
supersymmetric ground state exists, and to
analyze the spectrum and other properties of the
classical metastable states.
 There are many natural generalizations of this
system that can be studied using similar tools.