Emergent Spacetime 193If N = (Ic + 1)M, where Ic is an integer, then the duality cascade stops after k
steps, and we find a SU(M) x SU(2M) gauge theory. This IR gauge theory ex-
hibits a multitude of interesting effects visible in the dual supergravity background.
One of them is confinement, which follows from the fact that the warp factor h is
finite and non-vanishing at the smallest radial coordinate, r = 0, which roughly
corresponds to z = zmax in an effective 5-d approach (2). This implies that the qq
potential grows linearly at large distances. The confinement scale is proportional
to c2f3. The geometric transition that generates E is dual in the gauge theory to a
non-perturbative quantum deformation of the moduli space of vacua, which origi-
nates from dimensional transmutation. It breaks the 22, chiral R-symmetry, which
rotates the complex conifold coordinates wa, down to 22.
The string dual also incorporates the Goldstone mechanism due to a spontaneous
breaking of the U(1) baryon number symmetry [13]. Because of the N = 1 SUSY,
this produces a moduli space of confining vacua. In the SU(M) x SU(2M) gauge
theory there exist baryonic operators A = AyAy, B = BYBY, which satisfy the
“baryonic branch” relation AB = const. If the gauge theory were treated classically,
this constant would vanish and the baryon symmetry would be unbroken. In the
full quantum theory the constant arises non-perturbatively and deforms the moduli
space [14]. The warped deformed conifold of [lo] is dual to the locus Id1 = IBI
in the gauge theory. Remarkably, the more general “throat” backgrounds, the
resolved warped deformed conifolds corresponding to the entire baryonic branch,
were constructed in [15]. These backgrounds were further studied in [16] where
various observables were calculated along the baryonic branch. It was shown that
a D3-brane moving on a resolved warped deformed conifold has a monotonically
rising potential that asymptotes to a constant value at large radius. Therefore,
when such a construction is embedded into a string compactification, it may serve
as a model of inflationary universe, with the position of the 3-brane on the throat
playing the role of the inflaton field, as in [17].
Throughout its history, string theory has been intertwined with the theory of
strong interactions. The AdS/CFT correspondence [1-3] succeeded in making pre-
cise connections between conformal 4-dimensional gauge theories and superstring
theories in 10 dimensions. This duality leads to many dynamical predictions about
strongly coupled gauge theories. Extensions of the AdS/CFT correspondence to
confining gauge theories provide new geometrical viewpoints on such important
phenomena as chiral symmetry breaking, dimensional transmutation, and quantum
deformations of moduli spaces of supersymmetric vacua. They allow for studying
glueball spectra, string tensions, and other observables. The throat backgrounds
that arise in this context may have applications also to physics beyond the standard
model, and to cosmological modeling.