Research Interest of Sebastian Franco

      Publication 1: Fractional Branes and Dynamical Supersymmetry Breaking (URL)
      Publication 2: An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals (URL)
      Publication 3: D=4 Chiral String Compactifications from Intersecting Branes (URL)

    URL of Research: 

Statement of Interest:


  I have pursued various lines of research in String Theory.  The main
underlying focus has been on the construction of gauge theories and
the study of their dynamics using D- branes. My research ranges from
the quest of phenomenological constructions in String Theory to the
exploration of possible generalizations of known field theory
dualities. The following list offers a summary of the main
contributions of my work.
 

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Intersecting brane worlds
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 I have worked in the construction of intersecting brane models with
phenomenological features. In these models, different Standard Model
gauge interactions propagate on different (intersecting) brane worlds,
partially wrapped in extra dimensions. Quarks and leptons live at
brane intersections, and are located at points separated in the extra
dimensions. Replication of families arises from multiple brane
intersections. Hierarchical Yukawa couplings appear
naturally. Finally, the proton is stable due to discrete symmetries
arising from world-sheet selection rules, exact to all orders in
perturbation theory.
 
 These models have been steadily perfected since our original papers,
becoming at present one of the most successful constructions in string
phenomenology.  Furthermore, several of the ideas introduced with them
have also served as inspiration for non-String Theory model building.
 
 

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 D-branes on toric singularities, Toric Duality and generalizations
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 I have studied supersymmetric gauge theories arising on the
world-volume of D-branes transverse to algebraic
singularities. Dualities of the type of Seiberg Duality are easily
understood and derived when embedding the gauge theories in String
Theory.
 
 An interesting set of gauge theories is the one of those that live on
the world-volume of D3-branes probing toric singularities. Given a
geometry, these theories are not uniquely determined. Thus, by
considering D3-branes probing non-compact, toric, singular Calabi-Yau
manifolds we are lead to more than one low energy gauge theory
descriptions with the same toric geometry as their moduli space. This
phenomenon is the essence of Toric Duality, which is a generalization
of Seiberg Duality for theories with toric moduli spaces. It is a full
equivalence between distinct N=1, d=4 gauge theories in the IR limit.
Microscopic theories with different matter content and interactions
become indistinguishable when we consider the long distance physics
they describe. Part of my research has been devoted to improving our
understanding of Toric Duality.
 
 We developed a technique for deriving four dimensional gauge theories
on D3-branes on toric singularities based on (p,q) webs. This type IIB
construction is useful in defining 5d fixed points as well as studying
dynamics of 5d gauge theories, but also in describing toric varieties
and their associated 4d gauge theories. The gauge theory on the
world-volume of a D3-brane probing a toric singularity can be computed
using local mirror symmetry from the geometric information encoded in
the corresponding (p,q) web. This method enables an easy visualization
of the connections between different theories associated with the same
geometry as well as between theories for different singularities,
making the derivation of dual theories straightforward.
 
 

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 Duality cascades and duality walls
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Extending the AdS/CFT correspondence to theories with a small amount
of supersymmetry that are not scale invariant is of central
significance in order to make contact with realistic theories such as
QCD. With this goal in mind, we studied the non-conformal gauge
theories on D3-branes probing toric singularities that are constructed
by the addition of fractional branes. The RG flows associated with
these theories extend the well studied Klebanov- Strassler cascade. We
developed a general methodology that computes the beta functions,
including the contributions of anomalous dimensions. We applied this
framework to study gauge theories for the Zeroth Hirzebruch
surface. In this case, we found the existence of 'duality walls',
which correspond to an energy scale in the UV beyond which dualities
cannot proceed.
 
 Later, we extended the field theory analysis of such cascades,
finding analytical expressions describing the flows and duality
walls. We found evidence that such flows are often chaotic and show
self-similar fractal features.  For a gauge theory dual to CP^2 blown
up at a point, we found periodic and quasi-periodic behavior for the
gauge theory couplings that does not violate the a-conjecture.
Finally, we constructed supergravity duals for del Pezzos that matched
our field theory beta functions.
 
 

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 Gauge Theories for Sasaki-Einstein manifolds
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Recently, the Y^{p,q} and L^{a,b,c} families of 5d Sasaki- Einstein
metrics were constructed. These are infinite classes of spaces with
$S^2 \times S^3$ topology. The metric cones over these manifolds are
toric. We found the infinite families of N=1, 4d, superconformal
quiver gauge theories that are AdS/CFT dual to these explicit horizon
Sasaki-Einstein manifolds.
 
 We provided a general set of rules for extracting the data defining a
quiver gauge theory from a given toric Calabi- Yau singularity. Our
methods combine information from the geometry and topology of
Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We
performed many nontrivial checks of the AdS/CFT correspondence on
these theories, such as central charge and R-charge computations from
volume calculations on the string side and a- maximization on the
gauge theory side.
 
 

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Brane Dimers and Quiver Gauge Theories
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 We developed a technique that enables one to quickly compute an
infinite number of toric geometries and their dual quiver gauge
theories. The central object in this construction is a ``brane
tiling,'' which encodes the gauge group, matter content and tree-level
superpotential of the gauge theory. The brane tiling can be
interpreted as a physical configuration of D5-branes ending on an NS5-
brane wrapping a holomorphic curve. Brane tilings give the largest
class of N=1 quiver gauge theories yet studied.  The key point in this
approach is a one-to-one correspondence between perfect matchings in
the brane tiling and fields in the linear sigma model construction of
the toric moduli space.
 

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Fractional Branes and Dynamical Supersymmetry Breaking
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 We investigated the dynamics of fractional branes at toric
singularities. We found that generically the field theories on such
fractional branes show dynamical supersymmetry breaking, due to the
appearance of non- perturbative superpotentials. This happens when the
complex deformation associated with a given fractional brane is
obstructed. In special cases, one recovers the known cases of
supersymmetric infrared behaviors, associated to SYM confinement
(mapped to complex deformations of the dual geometries, in the
gauge/string correspondence sense) or N=2 fractional branes. In the
supersymmetry breaking cases, when the dynamics of closed string
moduli at the singularity is included, the theories show a runaway
behavior (involving moduli such as FI terms or equivalently dibaryonic
operators), rather than stable non-supersymmetric minima.
 
 
 I am working on extending the lines of research detailed above in
various directions. In addition, I am currently also involved in
projects dealing with:
 
 - Possible application of dimer model ideas to the determination of
gauge theories on D3-branes probing orientifolds of toric
singularities.
 
 - Gauge theory dual of closed string tachyon condensation on
non-supersymmetric orbifolds.