Baryon as impurity for phase transition in string landscape
Accepted: May
Baryon as impurity for phase transition in string
Aya Kasai 0 3
Yuichiro Nakai 0 1
Yutaka Ookouchi 0 2 3
Superstring Vacua
0 Cambridge , MA 02138 , U.S.A
1 Department of Physics, Harvard University
2 Faculty of Arts and Science, Kyushu University
3 Department of Physics, Kyushu University
We consider a decay of a false vacuum in ux compacti cations of type IIB string theory and study a catalytic e ect for a phase transition induced by a new type of impurities. We concentrate on the large N dual of a D5-brane/anti-D5-brane system which has a rich vacuum structure. We show that D3-branes wrapping the 3-cycles can form a baryon bound state with a monopole. We nd that these baryon-like objects can make the lifetime of the metastable vacuum shorter.
Brane Dynamics in Gauge Theories; D-branes; Flux compacti cations
1 Introduction 2
The brane/anti-brane system at large N
Review of geometrically induced metastable vacua
Phase transitions
2.2.1
2.2.2
Transitions between the N con ning vacua
Transitions reducing the RR
Baryon/monopole bound states
The catalytic e ects
Metastability of the vacuum with impurity
The decay rate
Conclusions and discussions
3
4
5
1
2.1
2.2
4.1
4.2
Introduction
Catalytic e ects for phase transitions are ubiquitous in nature. The evolution of the
universe (or multiverse) may be a ected by their existence in that the catalysts accelerate
transitions between vacua. In fact, it has been discussed in eld theories that a semi-classical
vacuum decay occurs from monopoles or cosmic strings [1{4] and applied to
phenomenological studies of metastable vacua [5{11]. Moreover, recent developments of string theory
compacti cations suggest the existence of the landscape of vacua [12{15]. Inspired by this
idea, non-supersymmetric vacua have been constructed in type IIB string theory, for
example see [15{22] (for a review, see [23]). Also in type IIA string theory, non-supersymmetric
vacua, which are related to metastable vacua in supersymmetric QCD [24], were realized in
the context of brane con gurations [25{28]. If the landscape really exists, it is necessary to
elucidate how e ectively phase transitions proceed in order to uncover the cosmic history.
As emphasized in [29, 30], catalytic e ects in string theory may play an important role
in this investigation. It was discussed in ref. [29] that stringy monopoles can accelerate
a decay of a non-supersymmetric vacuum, whose geometry is constructed from D5-branes
and anti-D5-branes wrapping homologous and minimal sized 2-spheres inside a Calabi-Yau
manifold [20]. The magnetic monopoles are realized by D3-branes wrapping a 3-chain
between D5/anti-D5-branes. In the decay process, the D3-branes form a bound state with a
domain wall D5-brane wrapping the 3-chain. It was shown that the stability of the false
vacuum depends on the strength of the magnetic ux induced by the dissolving D3-branes.
Thus, it would be important to study the catalytic e ect in ux compacti cations to extract
a lesson for the string landscape.
{ 1 {
The large N dual picture of this D5-brane/anti-D5-brane system is given by geometric
transition which replaces the wrapped 2-spheres with nite sized 3-spheres where
Ramond
Ramond (RR)
uxes are turned on [17, 20, 31]. Ref. [32] further analyzed the phase
structure of this system. In addition to classi cation of the vacua in terms of the number
of the ux lines through the 3-spheres, there are many metastable states with the same
number of the
ux lines, which can be interpreted as N con ning vacua present in the
N
= 1 SU(N ) pure Yang-Mills theory in the limit where branes and anit-branes are
in nitely separated. These N vacua are degenerate at the leading order in SUSY breaking
but higher order corrections, calculated by an auxiliary matrix model [35{37], lift this
degeneracy. Then, transitions between the vacua proceed by wrapping D5-branes over the
3-cycles in the manifold like brane/ ux annihilation [18] (See also refs. [38{42]).1 As in
the case of the open string picture, a D5-brane wrapping a compact 3-cycle connecting the
3-spheres is a domain wall solution for a vacuum decay reducing the number of the RR
ux lines. Furthermore, D5-branes wrapping the 3-spheres at tips of the conifold points
are domain walls separating the multiple con ning vacua.
In this paper, we consider the large N dual picture of the D5-brane/anti-D5-brane
system and study a catalytic e ect for a transition between the vacua from a new type of
impurities, a baryon bound state with a monopole. The existence of a baryon vertex was
rstly proposed by ref. [44] in the context of the AdS/CFT correspondence [45]. While a
stringy monopole is realized by wrapping a D3-brane over a compact 3-cycle as discussed in
ref. [29], the presence of background RR
uxes in a 3-sphere induces the charge of a gauge
eld on a wrapped D3-brane world-volume. Since the total charge of a gauge eld has to
vanish in a closed cycle, the D3-brane is attached by fun (...truncated)