Unbroken Group Research Articles

Restoring naturalness via conjugate fermions

We propose a novel mechanism for canceling the leading order contribution to the potential in composite Higgs scenarios. The mechanism relies on the splitting of a pseudoreal representation of the global symmetry into a complex representation and its conjugate of the unbroken group. We identify two cosets one of which includes a custodial symmetry. A numerical analysis is performed in a phenomenological three-site model and the resulting fine-tuning is analyzed. The canceling of the leading order potential results in a drastic reduction of the fine-tuning. For a symmetry breaking scale of the strong sector as high as f=1600 GeV, fine-tuning can be as good as 10% or even better. We discuss a possible interpretation in the 5D holographic dual. Unique signatures of the model include quarks with baryon number B=2/3 with highly distinctive decays which can be looked for at the LHC. Published by the American Physical Society 2024

Superconformal duality-invariant models and mathcal{N} = 4 SYM effective action

We present mathcal{N} = 2 superconformal U(1) duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the mathcal{N} = 4 SU(N) super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group SU(N) is spontaneously broken to SU(N − 1) × U(1); and (ii) the dynamics is captured by a single mathcal{N} = 2 vector multiplet associated with the U(1) factor of the unbroken group. Additionally, a local U(1) duality-invariant action generating the mathcal{N} = 2 super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed U(1) duality-invariant mathcal{N} = 1 superconformal electrodynamics, we introduce its SL(2, ℝ) duality-invariant coupling to the dilaton-axion multiplet.

The infrared structure of Nambu-Goldstone bosons

The construction of effective actions for Nambu-Goldstone bosons, and the nonlinear sigma model, usually requires a target coset space G/H. Recent progresses uncovered a new formulation using only IR data without reference to the broken group G in the UV, by imposing the Adler’s zero condition, which can be seen to originate from the superselection rule in the space of degenerate vacua. The IR construction imposes a nonlinear shift symmetry on the Lagrangian to enforce the correct single soft limit amid constraints of the unbroken group H. We present a systematic study on the consequence of the Adler’s zero condition in correlation functions of nonlinear sigma models, by deriving the conserved current and the Ward identity associated with the nonlinear shift symmetry, and demonstrate how the old-fashioned current algebra emerges. The Ward identity leads to a new representation of on-shell amplitudes, which amounts to bootstrapping the higher point amplitudes from lower point amplitudes and adding new vertices to satisfy the Adler’s condition. The IR perspective allows one to extract Feynman rules for the mysterious extended theory of biadjoint cubic scalars residing in the subleading single soft limit, which was first discovered using the Cachazo-He-Yuan representation of scattering amplitudes. In addition, we present the subleading triple soft theorem in the nonlinear sigma model and show that it is also controlled by on-shell amplitudes of the same extended theory as in the subleading single soft limit.

SO(10) thick branes and perturbative stability

Three self-gravitating $SO(10)$ domain walls in five dimensions are obtained and their properties are analyzed. These non-abelian domain walls interpolate between AdS${}_5$ spacetimes with different embedding of $SU(5)$ in $SO(10)$ and they can be distinguished, among other features, by the unbroken group on each wall, being either $SO(10)$, $SO(6)\otimes SU(2)\otimes U(1)/Z_2$ or $SU(4)\otimes SO(2)\otimes U(1)/Z_4$. We show that, unlike Minkowskian versions, the curved scenarios are perturbatively stable due to the gravitational capture of scalar fluctuations associated to the residual orthogonal subgroup in the core of the walls. These stabilizer modes are additional to the four-dimensional Nambu-Goldstone states found in two of the three gravitational sceanarios.

Adler’s zero and effective Lagrangians for nonlinearly realized symmetry

Long ago Coleman, Callan, Wess and Zumino (CCWZ) constructed the general effective lagrangian for nonlinearly realized symmetry by finding all possible nonlinear representations of the broken group G which become linear when restricted to the unbroken group H. However, in the case of a single Nambu-Goldstone boson (NGB), which corresponds to a broken U(1), the effective lagrangian can also be obtained by imposing a constant shift symmetry. In this work we generalize the shift symmetry approach to multiple NGBs and show that, when they furnish a linear representation of H that can be embedded in a symmetric coset, it is possible to derive the CCWZ lagrangian by imposing 1) the "Adler's zero condition," which requires scattering amplitudes to vanish when emitting a single soft NGB, and 2) closure of shift symmetry with the linearly realized symmetry; knowledge of the broken group G is not required at all. Using only generators of H, the NGB covariant derivative and the associated gauge field can be computed to all orders in the NGB decay constant f.

Charge quantization and the Standard Model from the [formula omitted] and [formula omitted] nonlinear σ-models

We investigate charge quantization in the Standard Model (SM) through a CP2 nonlinear sigma model (NLSM), SU(3)G/(SU(2)H×U(1)H), and a CP3 model, SU(4)G/(SU(3)H×U(1)H). We also generalize to any CPk model. Charge quantization follows from the consistency and dynamics of the NLSM, without a monopole or Grand Unified Theory, as shown in our earlier work on the CP1 model (arXiv:1309.0692). We find that representations of the matter fields under the unbroken non-abelian subgroup dictate their charge quantization under the U(1)H factor. In the CP2 model the unbroken group is identified with the weak and hypercharge groups of the SM, and the Nambu–Goldstone boson (NGB) has the quantum numbers of a SM Higgs. There is the intriguing possibility of a connection with the vanishing of the Higgs self-coupling at the Planck scale. Interestingly, with some minor assumptions (no vector-like matter and minimal representations) and starting with a single quark doublet, anomaly cancellation requires the matter structure of a generation in the SM. Similar analysis holds in the CP3 model, with the unbroken group identified with QCD and hypercharge, and the NGB having the up quark as a partner in a supersymmetric model. This can motivate solving the strong CP problem with a vanishing up quark mass.

Pionic dark matter

We study a phenomenological model where the lightest dark matter (DM) particles are the pseudo-Goldstone excitations associated with a spontaneously broken symmetry, and transforming linearly with respect to an unbroken group H. For definiteness we take H = SU(N) and assume the Goldstone particles are bosons; in parallel with QCD, we refer to these particles as dark-matter pions. This scenario is in contrast to the common assumption that DM fields transform linearly under the full symmetry of the model. We illustrate the formalism by treating in detail the case of H = SU(2), in particular we calculate all the interactions relevant for the Boltzmann equations, which we solve numerically; we also derive approximate analytic solutions and show their consistency with the numerical results. We then compare the results with the constraints derived from the cold DM and direct detection experiments and derive the corresponding restrictions on the model parameters.

Bound states in Script N = 4 SYM onT3: Spin(2n) and the exceptional groups

The low energy spectrum of (3+1)-dimensional N = 4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and elecric 't Hooft fluxes. At weak coupling, the wave-functions of these states are supported near points in the moduli space of flat connections where the unbroken gauge group is semi-simple. The number of such states is related to the number of normalizable bound states at threshold in the super symmetric matrix quantum mechanics wit h 1 6 supercharges based on this unbroken group. Mathematic ally, the determination of the spectrum relies on the classification of almost commuting triples with semi-simple centralizers. We complete the work begun in a previous paper, by computing the spectrum of bound states in theories based on the even-dimensional spin groups and the exceptional groups. The results satisfy the constraints of S-duality in a rather non-trivial way.

Low-energy spectrum of Script N = 4 super-Yang-Mills onT3: flat connections, bound states at threshold, andS-duality

We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions and discrete abelian magnetic and electric 't Hooft fluxes of the continua are computable in a semi-classical approximation. The wave-functions of the low-energy states are supported on submanifolds of the moduli space of flat connections, at which various subgroups of the gauge group are left unbroken. The field theory degrees of freedom transverse to such a submanifold are approximated by supersymmetric matrix quantum mechanics with 16 supercharges, based on the semi-simple part of this unbroken group. Conjectures about the number of normalizable bound states at threshold in the latter theory play a crucial role in our analysis. In this way, we compute the low-energy spectra in the cases where the simply connected cover of the gauge group is given by SU(n), Spin(2n+1) or Sp(2n). We then show that the constraints of S-duality are obeyed for unique values of the number of bound states in the matrix quantum mechanics. In the cases based on Spin(2n+1) and Sp(2n), the proof involves surprisingly subtle combinatorial identities, which hint at a rich underlying structure.

Self-dual effective action of N = 4 SYM revisited

More evidence is provided for the conjectured correspondence between the D3-brane action in AdS_5 x S^5 and the low-energy effective action for N = 4 SU(N) SYM on its Coulomb branch, where the gauge group SU(N) is spontaneously broken to SU(N-1) x U(1) and the dynamics is described by a single N = 2 vector multiplet corresponding to the U(1) factor of the unbroken group. Using an off-shell formulation for N = 4 SYM in N = 2 harmonic superspace, within the background-field quantization scheme we compute the two-loop quantum correction to a holomorphic sector of the effective action, which is a supersymmetric completion of interactions of the form \Omega ((F^+)^2 |Y|^{-4}) (F^+)^2(F^-)^2 |Y|^{-4}, with F^\pm the (anti) self-dual components of the U(1) gauge field strength, and Y the complex scalar belonging to the vector multiplet. In the one-loop approximation, \Omega was shown in hep-th/9911221 to be constant. It is demonstrated in the present paper that \Omega \propto (F^+)^2 |Y|^{-4} at the two-loop order. The corresponding coefficient proves to agree with the F^6 coefficient in the D3-brane action, after implementing the nonlinear field redefinition which was sketched in hep-th/9810152 and which relates the N = 2 vector multiplet component fields with those living on the D3-brane. In the approximation considered, our results are consistent with the conjecture of hep-th/9810152 that the N = 4 SYM effective action is self-dual under N = 2 superfield Legendre transformation, and also with the stronger conjecture of hep-th/0001068 that it is self-dual under supersymmetric U(1) duality rotations.

On low rank classical groups in string theory, gauge theory and matrix models

We consider N=1 supersymmetric U( N), SO( N), and Sp( N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature.

Instantons in partially broken gauge groups

We discuss the effects of instantons in partially broken gauge groups on the low-energy effective gauge theory. Such effects arise when some of the instantons of the original gauge group G are no longer contained in (or can not be gauge rotated into) the unbroken group H. In cases of simple G and H, a good indicator for the existence of such instantons is the “index of embedding.” However, in the general case one has to examine π 3( G/ H) to decide whether there are any instantons in the broken part of the gauge group. We give several examples of supersymmetric theories where such instantons exist and leave their effects on the low-energy effective theory.

Reduced fiber bundles and symmetries of gauge field theories rigid reductions and the einstein-cartan theory

The process of the reduction of a principal fibre bundle P(M, G) to a reduced subbundle Q(M, H) is analysed in view of applications to the description of symmetries of gauge theories. The main idea is to relate symmetries of the nonuniqueness of the reduction by gauging the different ways in which for each fiber the unbroken group H is imbedded into the large group G. Gauge theories encompassing gravitation are especially taken into account.