arXiv subjects

Iñaki García-Etxebarria

Publications and source records attributed to Iñaki García-Etxebarria.

At least 19 recordsLinked to original sources

arXiv2020

Dai-Freed anomalies in particle physics

Anomalies can be elegantly analyzed by means of the Dai-Freed theorem. In this framework it is natural to consider a refinement of traditional anomaly cancellation conditions, which sometimes leads to nontrivial extra constraints in the fermion spectrum. We analyze these more refined anomaly cancellation conditions in a variety of theories of physical interest, including the Standard Model and the $SU(5)$ and $Spin(10)$ GUTs, which we find to be anomaly free. Turning to discrete symmetries, we find that baryon triality has a $\mathbb{Z}_9$ anomaly that only cancels if the number of generations is a multiple of 3. Assuming the existence of certain anomaly-free $\mathbb{Z}_4$ symmetry we relate the fact that there are 16 fermions per generation of the Standard Model - including right-handed neutrinos - to anomalies under time-reversal of boundary states in four-dimensional topological superconductors. A similar relation exists for the MSSM, only this time involving the number of gauginos and Higgsinos, and it is non-trivially, and remarkably, satisfied for the $SU(3)\times SU(2) \times U(1)$ gauge group with two Higgs doublets. We relate the constraints we find to the well-known Ibañez-Ross ones, and discuss the dependence on UV data of the construction. Finally, we comment on the (non-)existence of K-theoretic $θ$ angles in four dimensions.

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arXiv2019

IIB flux non-commutativity and the global structure of field theories

We discuss the origin of the choice of global structure for six dimensional $(2,0)$ theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of $\mathcal{N}=4$ theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of $\mathcal{N}=4$ ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional $(1,0)$ theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects.

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arXiv2019

A Note on Non-Flat Points in the $SU(5)\times U(1)$ PQ F-Theory Model

Non-flat fibrations often appear in F-theory GUT models, and their interpretation is still somewhat mysterious. In this note we explore this issue in a model of particular phenomenological interest, the global $SU(5)\times U(1)$ Peccei-Quinn F-theory model. We present evidence that co-dimension three non-flat fibres give rise to higher order couplings in the effective four-dimensional superpotential. More specifically, in our example we find $\mathbf{10}\, \mathbf{5}\, \mathbf{5}\, \mathbf{5}$ couplings.

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arXiv2017

Non-geometric heterotic backgrounds and 6D SCFTs/LSTs

We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of non-geometric backgrounds of the $E_8\times E_8$ and the $\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. The majority of the resulting dual threefolds turn out to contain singularities which do not admit a crepant resolution. When the singularities can be resolved crepantly, the theories living on the defect are explicitly determined and reveal a form of duality in which distinct defects are described by the same IR fixed point. In particular, a subclass of non-geometric defects corresponds to SCFTs/LSTs arising from small heterotic instantons on ADE singularities.

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arXiv2017

Exceptional $\mathcal N=3$ theories

We present a new construction of four dimensional $\mathcal N=3$ theories, given by M5 branes wrapping a $T^2$ in an M-theory U-fold background. The resulting setup generalizes the one used in the usual class $\mathcal S$ construction of four dimensional theories by using an extra discrete symmetry on the M5 worldvolume. Together with the M-theory U-fold description of $(0,2)$ $E$-type six-dimensional SCFTs, this allows to construct new, exceptional, $\mathcal N=3$ theories.

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arXiv2017

2d orbifolds with exotic supersymmetry

We analyse various two dimensional theories arising from compactification of type II and heterotic string theory on asymmetric orbifolds. We find extra supersymmetry generators arising from twisted sectors, giving rise to exotic supersymmetry algebras. Among others we discover new cases with a large number of supercharges, such as $\mathcal{N}=(20,8)$, $\mathcal{N}=(24,8)$, $\mathcal{N}=(32,0)$, $\mathcal{N}=(24,24)$ and $\mathcal{N}=(48,0)$.

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arXiv2017

Global Orientifolded Quivers with Inflation

We describe global embeddings of fractional D3 branes at orientifolded singularities in type IIB flux compactifications. We present an explicit Calabi-Yau example where the chiral visible sector lives on a local orientifolded quiver while non-perturbative effects, $α'$ corrections and a T-brane hidden sector lead to full closed string moduli stabilisation in a de Sitter vacuum. The same model can also successfully give rise to inflation driven by a del Pezzo divisor. Our model represents the first explicit Calabi-Yau example featuring both an inflationary and a chiral visible sector.

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arXiv2017

8d gauge anomalies and the topological Green-Schwarz mechanism

String theory provides us with 8d supersymmetric gauge theory with gauge algebras $\mathfrak{su}(N)$, $\mathfrak{so}(2N)$, $\mathfrak{sp}(N)$, $\mathfrak{e}_{6}$, $\mathfrak{e}_{7}$ and $\mathfrak{e}_{8}$, but no construction for $\mathfrak{so}(2N{+}1)$, $\mathfrak{f}_4$ and $\mathfrak{g}_2$ is known. In this paper, we show that the theories for $\mathfrak{f}_4$ and $\mathfrak{so}(2N{+}1)$ have a global gauge anomaly associated to $π_{d=8}$, while $\mathfrak{g}_2$ does not have it. We argue that the anomaly associated to $π_d$ in $d$-dimensional gauge theories cannot be canceled by topological degrees of freedom in general. We also show that the theories for $\mathfrak{sp}(N)$ have a subtler gauge anomaly, which we suggest should be canceled by a topological analogue of the Green-Schwarz mechanism.

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arXiv2017

$\mathcal N=3$ four dimensional field theories

We briefly review a class of four dimensional $\mathcal N=3$ field theories constructed by taking a quotient of $\mathcal N=4$ SYM with gauge group $U(N)$. The quotient involves a discrete symmetry that only exists for specific, order one, values of the coupling constant, so the resulting theories are intrinsically strongly coupled. These theories admit a simple realization in string theory as the worldvolume theory of a stack of D3 branes probing a generalized orientifold plane, or S-fold. Their holographic dual is given by a non-trivial F-theory fibration over $AdS_5 \times S^5/\mathbb Z_k$ which is weakly curved but with the string coupling frozen at an order one value.

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arXiv2017

N=3 four dimensional field theories

We introduce a class of four dimensional field theories constructed by quotienting ordinary $\mathcal{N}=4$ $U(N)$ SYM by particular combinations of R-symmetry and $SL(2,\mathbb{Z})$ automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large $N$ limit described by a non-trivial F-theory fibration with base $AdS_5\times (S^5/\mathbb{Z}_k)$. Upon reduction on a circle the $\mathcal{N}=3$ theories flow to well-known $\mathcal{N}=6$ ABJM theories.

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arXiv2016

$E_6$ Yukawa couplings in F-theory as D-brane instanton effects

In a weak coupling limit the neighborhood of $E_6$ Yukawa points in $SU(5)$ GUT F-theory models is described by a non-resolvable orientifold of the conifold. We explicitly show, first directly in IIB and then via a mirror symmetry argument, that in this limit the $E_6$ Yukawa coupling is better described as coming from the non-perturbative contribution of a euclidean D1-brane wrapping the non-resolvable cycle. We also discuss how the M-theory description interpolates between the weak and strong coupling viewpoints.

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arXiv2016

S-duality in $\mathcal{N} = 1$ orientifold SCFTs

We present a general solution to the problem of determining all S-dual descriptions for a specific (but very rich) class of $\mathcal{N} = 1$ SCFTs. These SCFTs are indexed by decorated toric diagrams, and can be engineered in string theory by probing orientifolds of isolated toric singularities with D3 branes. The S-dual phases are described by quiver gauge theories coupled to specific types of conformal matter which we describe explicitly. We illustrate our construction with many examples, including S-dualities in previously unknown SCFTs.

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arXiv2016

Ubiquity of non-geometry in heterotic compactifications

We study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest non-trivial elliptic fibration the effect is quite dramatic: the $I_1$ degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the $T^2$. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety due to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.

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arXiv2016

Heterotic T-fects, 6D SCFTs, and F-Theory

We study the $(1,0)$ six-dimensional SCFTs living on defects of non-geometric heterotic backgrounds (T-fects) preserving a $E_7\times E_8$ subgroup of $E_8\times E_8$. These configurations can be dualized explicitly to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. We find that the majority of the resulting dual threefolds contain non-resolvable singularities. In those cases in which we can resolve the singularities we explicitly determine the SCFTs living on the defect. We find a form of duality in which distinct defects are described by the same IR fixed point. For instance, we find that a subclass of non-geometric defects are described by the SCFT arising from small heterotic instantons on ADE singularities.

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arXiv2016

Global String Embeddings for the Nilpotent Goldstino

We discuss techniques for embedding a nilpotent Goldstino sector both in weakly coupled type IIB compactifications and F-theory models at arbitrary coupling, providing examples of both scenarios in semi-realistic compactifications. We start by showing how to construct a local embedding for the nilpotent Goldstino in terms of an anti D3-brane in a local conifold throat, and then discuss how to engineer the required local structure in globally consistent compact models. We present two explicit examples, the last one supporting also chiral matter and Kähler moduli stabilisation.

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arXiv2015

Closed tachyon solitons in type II string theory

Type II theories can be described as the endpoint of closed string tachyon condensation in certain orbifolds of supercritical type 0 theories. In this paper, we study solitons of this closed string tachyon and analyze the nature of the resulting defects in critical type II theories. The solitons are classified by the real K-theory groups KO of bundles associated to pairs of supercritical dimensions. For real codimension 4 and 8, corresponding to $KO({\bf S}^4)={\bf Z}$ and $KO({\bf S}^8)={\bf Z}$, the defects correspond to a gravitational instanton and a fundamental string, respectively. We apply these ideas to reinterpret the worldsheet GLSM, regarded as a supercritical theory on the ambient toric space with closed tachyon condensation onto the CY hypersurface, and use it to describe charged solitons under discrete isometries. We also suggest the possible applications of supercritical strings to the physical interpretation of the matrix factorization description of F-theory on singular spaces.

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arXiv2015

Strongly coupled phases of $\mathcal{N}=1$ S-duality

We analyze S-duality of orientifolds of the Calabi-Yau cone over the first del Pezzo surface ($dP_1$). The S-duals of known phases, described by quiver gauge theories, contain intrinsically strongly-coupled sectors. These sectors are realized by a higher multiplicity intersection of NS5 branes and D5 branes atop an O5 plane, and can be thought of as stuck at the infinite coupling point between two Seiberg-dual gauge theories. We argue that such sectors appear generically in orientifolds of non-orbifold singularities, where in many examples every orientifold phase contains such a sector. Understanding such sectors is therefore key to understanding orientifolds of Calabi-Yau singularities. We construct the strongly-coupled sectors for $dP_1$ orientifolds using deconfinement, and show that they have interesting, non-trivial properties. Using this construction, we verify the predictions of S-duality for $dP_1$.

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arXiv2014

Special Points of Inflation in Flux Compactifications

We study the realisation of axion inflation models in the complex structure moduli spaces of Calabi-Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure point and conifold point, but can be of more general nature. In Type IIB and F-theory compactifications the geometric axions receive a scalar potential from a flux-induced superpotential. We find toy variants of various inflationary potentials including the ones for natural inflation of one or multiple axions, or axion monodromy inflation with polynomial potential. Interesting examples are also given by mirror geometries of torus fibrations with Mordell-Weil group of rank $N-1$ or an $N$-section, which admit an axion if $N>3$.

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