We argue a smallness of gauge couplings in abelian quiver gauge theories, taking the anomaly cancellation condition into account. In theories of our interest there exist chiral fermions leading to chiral gauge anomalies, and an anomaly-free gauge coupling tends to be small, and hence can give a non-trivial condition of the weak gravity conjecture. As concrete examples, we consider $U(1)^{k}$ gauge theories with a discrete symmetry associated with cyclic permutations between the gauge groups, and identify anomaly-free $U(1)$ gauge symmetries and the corresponding gauge couplings. Owing to this discrete symmetry, we can systematically study the models and we find that the models would be examples of the weak coupling conjecture. It is conjectured that a certain class of chiral gauge theories with too many $U(1)$ symmetries may be in the swampland. We also numerically study constraints on the couplings from the scalar weak gravity conjecture in a concrete model. These constraints may have a phenomenological implication to model building of a chiral hidden sector as well as the visible sector.
We extend the proposal of Berenstein, Maldacena and Nastase to Type IIB superstring propagating on pp-wave over ${\bf R}^4/{\bf Z}_k$ orbifold. We show that first-quantized free string theory is described correctly by the large $N$, fixed gauge coupling limit of ${\cal N}=2$ $[U(N)]^k$ quiver gauge theory. We propose a precise map between gauge theory operators and string states for both untwisted and twisted sectors. We also compute leading-order perturbative correction to the anomalous dimensions of these operators. The result is in agreement with the value deduced from string energy spectru…
We consider four-dimensional N=2 superconformal field theories based on ADE quiver diagrams. We use the procedure of hep-th/0206079 and compute the exact anomalous dimensions of operators with large U(1)_R charge to all orders in perturbation in the planar limit. The results are in agreement with the string computation in the dual pp-wave backgrounds.
Many conformal quiver gauge theories admit nonconformal generalizations. These generalizations change the rank of some of the gauge groups in a consistent way, inducing a running in the gauge couplings. We find a group of discrete transformation that acts on a large class of these theories. These transformations form a central extension of the Heisenberg group, generalizing the Heisenberg group of the conformal case, when all gauge groups have the same rank. In the AdS/CFT correspondence the nonconformal quiver gauge theory is dual to supergravity backgrounds with both five-form and three-form…
We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kaehler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of "multiplicities". We explain in detail how to decompose the …
A generic feature of string-derived models is the appearance of an anomalous Abelian U(1)_A symmetry which, among other properties, constrains the Yukawa couplings and distinguishes the three families from each other. In this paper, we discuss in a model-independent way the general constraints imposed by such a U(1)_A symmetry on fermion masses, R-violating couplings and proton-decay operators in a generic flipped SU(5) x U(1)' model. We construct all possible viable fermion mass textures and give various examples of effective low-energy models which are distinguished from each other by their …
We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of $\mathcal{N}=2$ superconformal field …
D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of the currently fashionable techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, finitude and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then we utilise certain results from graph …
Global consistency of string compactifications places constraints on the chiral matter spectrum of a gauge theory which include those necessary for the absence of cubic nonabelian anomalies, but also contain some additional conditions. In the class of theories we study, some of these are present in a field theory augmented by anomalous U(1)'s and Chern-Simons terms, but some are genuinely not present in field theory. Their violation has phenomenological implications, rendering inconsistent many quiver gauge theories with the chiral matter spectrum of the MSSM. The inconsistent MSSM quivers oft…
The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-$N$ limit, at least for vector-like models. The validity of chiral-like models is not established yet, due to technical problems in both analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested that the counting of chiral operators can be used to find the eigenvalue distribution of quiver matrix models. In this paper we apply this method to some vector-like or chiral-like quiver theories, including the triangul…
We prove a set of identities for the anomalous dimensions of the quark and gluon conformal operators in the flavour singlet channel in QCD. These relations arise from the graded commutator algebra of the N=1 superconformal group. We evaluate the rotation matrices for the quantities under study from the conventional dimensional regularization to the supersymmetry preserving regularization scheme. Using them we verify the equalities in two-loop approximation employing the results for the NLO anomalous dimensions of the conformal operators in the minimal subtraction scheme derived earlier.
We study the correspondence between AdS$_3$ massive IIA supergravity vacua and two-dimensional $\mathcal{N}=(0,4)$ quiver quantum field theories. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space which provide the dual quiver theory with exactly the correct amount of flavor symmetry in order to cancel its gauge anomalies. Then we propose that the structure of the field theory should be complemented with additional bifundamental matte…
Topological spin liquids can be described by topological gauge theories with global symmetry. Due to the presence of both nontrivial bulk deconfined gauge fluxes and global symmetry, topological spin liquids are examples of the so-called "Symmetry Enriched Topological phases" (SET). In this paper, we find that, in some twisted versions of topological gauge theories (with discrete Abelian gauge group $G_g$), implementing a global symmetry (denoted by $G_s$) is anomalous although symmetry charge carried by topological point-like excitations is normally fractionalized and classified by the second…
We study gauge theories where quasi-hidden sectors are added to the MSSM for the sake of string consistency conditions which would otherwise not be satisfied. We focus on quiver gauge theories motivated by weakly coupled type II orientifold compactifications. Model independent features in this class include an anomalous U(1)_V symmetry which protects messenger masses and has strong consequences for superpotential couplings, a rich phenomenology of heavy and light Z' bosons, and axionic couplings required for anomaly cancellation via the Green-Schwarz mechanism. We discuss possibilities for dar…
We show that supersymmetry is anomalous in ${\cal N}=1$ superconformal quantum field theories (SCFTs) with an anomalous R-symmetry. This anomaly was originally found in holographic SCFTs at strong coupling. Here we show that this anomaly is present in general and demonstrate it for the massless superconformal Wess-Zumino model via a one loop computation. The anomaly appears first in four-point functions of two supercurrents with either two R-currents or with an R-current and an energy momentum tensor. In fact, the Wess-Zumino consistency conditions together with the standard R-symmetry anomaly…
Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge theories. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in N=4 super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth -- at most, it can grow a power of `t Hooft coupling. For theory with gauge group SU(N) x SU(N) and bifundamental hypermultiplets, the…
Implications of inserting a conformal, monodromy line defect in three dimensional O($N$) models are studied. We consider then the WF O($N$) model, and study the two-point Green's function for bulk-local fields found from both the bulk-defect expansion and Feynman diagrams. This yields the anomalous dimensions for bulk- and defect-local primaries as well as one of the OPE coefficients as $ε$-expansions to the first loop order. As a check on our results, we study the $(ϕ^k)^2ϕ^j$ operator both using the bulk-defect expansion as well as the equations of motion.
We investigate the anomalous creation of fundamental strings using the boundary state formalism of fractional D-branes on ALE spaces in the orbifold limit. The open string Witten index plays a crucial role in this calculation and so the result remains unchanged even if we blow up the orbifold geometrically, matching the anomaly inflow argument. Further we consider the quiver gauge theories on such fractional D3-branes and see that the string creation mechanism determines 1-loop logarithmic monodromy of these gauge theories. Also we comment on the relation of D(-1)-D3 amplitude to the 1-loop be…
In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantum mechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for non-zero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of $\mat…
In (1+1) dimensional hydrodynamics in presence of the gravitational anomalies, the constitutive relations for the stress tensor contain the response parameters $\bar{C}_1$, $\bar{C}_2$ and the gravitation anomaly coefficients $c_g$, $c_w$. Here it is shown that they are related by the two relations $\bar{C}_1 = 4π^2 c_w$ and $\bar{C}_2 = 8π^2 c_g$. This agrees with the earlier findings. I argue that the Israel-Hartle-Hawking vacuum is the natural boundary condition which leads to such relation. Finally, the possible physical implications are discussed.
In the same base setup as Sakharov's induced gravity, we investigate emergence of gravity in effective quantum field theories (QFT), with particular emphasis on the gauge sector in which gauge bosons acquire anomalous masses in proportion to the ultraviolet cutoff $Λ_\wp$. Drawing on the fact that $Λ_\wp^2$ corrections explicitly break the gauge and Poincare symmetries, we find that it is possible to map $Λ_\wp^2$ to spacetime curvature as a covariance relation and we find also that this map erases the anomalous gauge boson masses. The resulting framework describes gravity by the general relat…
Observations show that, at the beginning of their existence, neutron stars are accelerated briskly to velocities of up to $1000$ km/s. We discuss possible mechanisms contributing to these kicks in a systematic effective-field-theory framework. Anomalies of the underlying microscopic theory result in chiral transport terms in the hydrodynamic description, and we identify these as explanation for the drastic acceleration. In the presence of vorticity or a magnetic field, the chiral transport effects cause neutrino emission along the respective axes. In typical scenarios, the transport effect due…
