Invariant Sector Research Articles

Symmetry-Enforced Entanglement in Maximally Mixed States

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is “strongly symmetric,” i.e., it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS) and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g., SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically with the number of qudits N. Published by the American Physical Society 2024

Gauge-invariant quantum fields

Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant description of the Higgs mode via a propagating gauge-invariant field. The renormalization of the model is studied in the Algebraic Renormalization approach. The decomposition of Slavnov–Taylor identities into separately invariant sectors is analyzed. We also comment on some non-renormalizable extensions of the model whose 1-PI Green’s functions are the flows of certain differential equations of the homogeneous Euler type, exactly resumming the dependence on a certain set of dim. 6 and dim. 8 derivative operators. The latter are identified uniquely by the condition that they span the mass and kinetic terms in the gauge-invariant dynamical fields. The construction can be extended to non-Abelian gauge groups.

Euclidean flows, solitons, and wormholes in AdS space from M-theory

Multiparametric families of nonsupersymmetric EAdS4 flows as well as asymptotically EAdS4 solitons and wormholes are constructed within the four-dimensional SO(8) gauged supergravity that describes the compactification of M-theory on S7. More concretely, the solutions are found within the so-called STU model that describes the U(1)4 invariant sector of the theory. The on-shell action and gravitational free energy are computed for the regular solutions, the latter being zero for the wormholes irrespective of supersymmetry. There are special loci in parameter space yielding solutions with enhanced (super)symmetry. Examples include a supersymmetric EAdS4 flow with SO(4)×SO(4) symmetry dual to a specific real mass deformation of ABJM on S3 as well as a nonsupersymmetric wormhole with SU(3)×U(1)2 symmetry. Uplift formulas for these and other examples to Euclidean solutions of 11-dimensional supergravity are presented and their complex nature discussed. Published by the American Physical Society 2024

Consistent truncation of eleven-dimensional supergravity on S8× S1

Eleven-dimensional supergravity on S8 × S1 is conjectured to be dual to the M-theory matrix model. We prove that the dynamics of a subset of fluctuations around this background is consistently described by D = 2 SO(9) gauged maximal supergravity. We provide the full non-linear uplift formulæ for all bosonic fields. We also present a further truncation to the SO(3)×SO(6) invariant sector and discuss its relation to the BMN matrix model at finite temperature. The construction relies on the framework of generalised Scherk-Schwarz reductions, established for E9 exceptional field theory in a companion paper. As a by-product, we severely constrain the most general gauge deformations in D = 2 admitting an uplift to higher dimensions.

Aspects of dynamical cobordism in AdS/CFT

The cobordism conjecture implies that consistent theories of Quantum Gravity must admit the introduction of boundaries. We study the dynamical realization of the cobordism conjecture in type IIB in AdS5 × S5, using the existing gravity duals of 4d \U0001d4a9 = 4 SYM with Gaiotto-Witten superconformal boundary conditions (near-horizon limits of D3-branes ending on NS5- and D5-branes). We show that these configurations are, from the 5d perspective, dynamical cobordism solutions which start from an asymptotic AdS5 vacuum and evolve until they hit an end of the world (ETW) brane with AdS4 worldvolume. The latter displays localization of gravity, and provide a completion of the Karch-Randall (KR) AdS branes, in which the backreaction of running scalars replace the KR cusp in the warp factor with a smooth bump. The dynamical scalars are either in the SO(6) invariant AdS5 bulk sector (e.g. describing the S5 size and its shrinking at the cobordism boundary) or brane localized (e.g. the SO(6) SO(3) × SO(3) squashing due to boundary conditions). We introduce a novel double scaling limit which zooms into the ETW brane and makes localization of gravity manifest, and which shows a tantalizing relation with wedge holography. We extend the picture to AdS5 theories with less (super)symmetry, via orbifolds and S-folds, leading to dynamical cobordisms for gravity duals of 4d theories with \U0001d4a9 = 2 and \U0001d4a9 = 3 supersymmetry.

Permutation symmetry in large- N matrix quantum mechanics and partition algebras

We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11-parameter permutation invariant quantum matrix harmonic oscillator Hamiltonian and calculate the canonical partition function. The permutation invariant sector of the Hilbert space, for general Hamiltonians, can be described using partition algebra diagrams forming the bases of a tower of partition algebras ${P}_{k}(N)$. The integer $k$ is interpreted as the degree of matrix oscillator polynomials in the quantum mechanics. Families of interacting Hamiltonians are described which are diagonalized by a representation theoretic basis for the permutation invariant subspace which we construct for $N\ensuremath{\ge}2k$. These include Hamiltonians for which the low-energy states are permutation invariant and can give rise to large ground state degeneracies related to the dimensions of partition algebras. A symmetry-based mechanism for quantum many body scars discussed in the literature can be realized in these matrix systems with permutation symmetry. A mapping of the matrix index values to lattice sites allows a realization of the mechanism in the context of modified Bose-Hubbard models. Extremal correlators analogous to those studied in $\mathrm{AdS}/\mathrm{CFT}$ are shown to obey selection rules based on Clebsch-Gordan multiplicites (Kronecker coefficients) of symmetric groups.

Switching controller for nonlinear systems: an invariant [K, KL] sector approach*

This paper addresses the invariant sector as a special class of sector that holds the invariant characteristics with some appropriate control input, i.e. the energy of the system drastically decreases and state trajectory always remains inside the sector once it moves into it by the suitable control signal. The analysis of the nonlinear sector is regarded in comparison function prospective to outreach the property of uniformity. Here, the construction of sector and invariant sector relies on the selection of well-suited control-Lyapunov function. The switching control with invariant sector is designed to ensure the state trajectories move inside the nonlinear sector in finite-time and stay inside for all future time. Finally, the effectiveness of the proposed algorithm is illustrated with real physical examples.

Black hole superpotential as a unifying entropy function and BPS thermodynamics

We develop an effective superpotential formalism for the SU(2)×U(1) invariant sector of mathcal{N} = 2 gauged supergravity in five dimensions with a U(1)3 Fayet-Iliopoulos gauging, and determine the exact superpotential that describes all 1/4 BPS solutions in this sector. This includes the Gutowski-Reall black holes, but also a much broader class of solutions with a squashed S3, magnetic flux and vector multiplet sources, as well as complex Euclidean BPS saddles. Some of these solutions are known only numerically, but the exact superpotential allows us to analytically evaluate the on-shell action, holographic one-point functions and conserved charges of all BPS solutions and to study their thermodynamics. In particular, by examining the supersymmetry Ward identities we show that solutions with supersymmetric vector multiplet sources break supersymmetry spontaneously. We also demonstrate the first law for black holes in the SU(2)×U(1) invariant sector and show that the conserved charges of supersymmetric solutions satisfy the generalized BPS relation derived in [1], which includes the supersymmetric Casimir energy as a consequence of the anomalous supersymmetry transformation of the mathcal{N} = 1 supercurrent at the boundary. Finally, we show that the effective superpotential provides a unifying entropy extremization principle, reproducing Sen’s entropy function for near extremal black holes and the Hosseini-Hristov-Zaffaroni functional for complex Euclidean BPS saddles.

Janus solutions from dyonic ISO(7) maximal gauged supergravity

We give a large class of new supersymmetric Janus solutions in dyonic ISO(7) maximal gauged supergravity encompassing all known solutions appearing recently. We consider SO(3) invariant sector in which the gauged supergravity admits four supersymmetric AdS4 vacua with N = 1, 1, 2, 3 unbroken supersymmetries and G2, SU(3), SU(3) × U(1) and SO(4) symmetries, respectively. We find Janus solutions preserving N = 1, 2, 3 supersymmetries and interpolating between AdS4 vacua and the N = 8 SYM phase. These solutions can be interpreted as conformal interfaces between SYM and various conformal phases of the dual field theory in three dimensions. The solutions can also be embedded in massive type IIA theory by a consistent truncation on S6. We also find a number of singular Janus solutions interpolating between N = 8 SYM or AdS4 vacua and singularities or between singular geometries. It turns out that, apart from the SYM phase on D2-branes, all the singularities arising in these solutions are unphysical in both four- and ten-dimensional frameworks.

Hamilton–Jacobi approach for linearly acceleration-dependent Lagrangians

We develop a constructive procedure for arriving at the Hamilton–Jacobi framework for the so-called affine in acceleration theories by analysing the canonical constraint structure. We find two scenarios in dependence of the order of the emerging equations of motion. By properly defining generalized brackets, the non-involutive constraints that originally arose, in both scenarios, may be removed so that the resulting involutive Hamiltonian constraints ensure integrability of the theories and, at the same time, lead to the right dynamics in the reduced phase space. In particular, when we have second-order derivatives equations of motion we are able to detect the gauge invariant sector of the theory by using a suitable approach based on the projection of the Hamiltonians onto the tangential and normal directions of the congruence of curves in the configuration space. Regarding this, we also explore the generators of canonical and gauge transformations of these theories. Further, we briefly outline how to determine the Hamilton principal function S for some particular setups. We apply our findings to some representative theories: a Chern–Simons-like theory in (2+1)-dim, an harmonic oscillator in 2D and, the geodetic brane cosmology emerging in the context of extra dimensions.

Many-Body Scars as a Group Invariant Sector of Hilbert Space.

We present a class of Hamiltonians H for which a sector of the Hilbert space invariant under a Lie group G, which is not a symmetry of H, possesses the essential properties of many-body scar states. These include the absence of thermalization and the "revivals" of special initial states in time evolution. A particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of N sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of N+1 scar states. One of these families, which was found in recent literature, comprises the well-known η-pairing states. We find another family of scar states that is U(N) invariant. Both families and most of the group-invariant scar states produced by our construction, in general, give rise to the off-diagonal long range order, which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored nonlocally and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states, which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group G and can be made exponentially large.

Lowest energy states of an O(N) fermionic chain

A quite general finite-size chain of fermions with $N$ internal degrees of freedom (flavors) and $O(N)$ symmetry is considered. In the case of the free boundary condition, we prove that the ground state in the invariant sector having exactly $m$ flavors with an odd particle number is represented by a single rank-$m$ antisymmetric multiplet. For the even-length chains, its particle-hole quantum number (if it's a good one) is given by the parity of the $m$. For the odd-length chains, the particle-hole symmetry leads to the twofold degeneracy among the conjugate multiplets. Similar statements are proven for the $O(N)$ mixed-spin chains in antisymmetric representations. The results are extended to the long-range interacting fermions and (partially) to the translation invariant chains.

(Four) Dual Plaquette 3D Ising Models.

A characteristic feature of the plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the plaquette Ising and the X-Cube model is similar to that between the quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

Classifying and constraining local four photon and four graviton S-matrices

We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants s, t and u. We construct these modules for every value of the spacetime dimension D, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by s2 at fixed t. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for D ≤ 6. For D ≥ 7 there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for D ≤ 6. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also violates our conjectured Regge growth bound, at least when D ≤ 6, even when the exchanged particles have low spin.

Stock Liquidity, Financial Report Quality, Wedge, and The Propensity to Pay Dividend

This research examined the effect of stock liquidity on the propensity to pay dividend for 254 Indonesian public listed firms during the period of l 2011 and 2015. Stock liquidity implies transparency level and serves as market monitor for management performance in using the cash flow. Furthermore, this research examines the impact of stock liquidity on dividend payment in the presence of agency conflicts using agency proxies, wedge and government ownership. This paper employed multivariate probit regression. The baseline model has controlled for time in-variant and industry sectors. Robustness checks are employed to present consistent result for other stock liquidity measures. The results confirm the predicted dividend model outcome and prove the contradiction in dividend signaling theory.

S-folds and (non-)supersymmetric Janus solutions

The S-fold description of Janus-type solutions of type IIB supergravity is investigated. This is done by first studying a U(1) × U (1) invariant sector of the four­ dimensional dyonically-gauged [SO(1) × SO(6)] × ℝ12 maximal supergravity that arises upon reduction of type IIB supergravity on ℝ × S5. Two AdS4 solutions preserving SU(3) and SO (6) gauge symmetry together with mathcal{N} = 1 and mathcal{N} = 0 supersymmetry are found within this sector. Fetching techniques from the E 7(7) exceptional field theory, these solutions are uplifted to ten-dimensional S-folds of type IIB Janus-type solutions of the form AdS4 × ℝ × M5. The solutions presented here are natural candidates for the holographic duals of three-dimensional mathcal{N} = 1 and mathcal{N} = 0 interface super-Yang-Mills theories with SU(3) and SU(4) internal symmetry.

Embedding the SU(3) sector of SO(8) supergravity in D=11

The SU(3)--invariant sector of maximal supergravity in four dimensions with an SO(8) gauging is uplifted to $D=11$ supergravity. In order to do this, the SU(3)--neutral sector of the tensor and duality hierarchies of the $D=4$ ${\cal N}=8$ supergravity is first worked out. The consistent $D=11$ embedding of the full, dynamical SU(3) sector is then expressed at the level of the $D=11$ metric and three-form gauge field in terms of these $D=4$ tensors. The redundancies introduced by this approach are eliminated at the level of the $D=11$ four-form field strength by making use of the $D=4$ duality hierarchy. Our results encompass previously known truncations of $D=11$ supergravity down to sectors of SO(8) supergravity with symmetry larger than SU(3), and include new ones. In particular, we obtain a new consistent truncation of $D=11$ supergravity to minimal $D=4$ ${\cal N}=2$ gauged supergravity.

Revisiting Lorentz violation in Hořava gravity

In the context of Horava gravity, the most promising known scenarios to recover Lorentz invariance at low energy are the possibilities that (1) the renormalization group flow of the system leads to emergent infrared Lorentz invariance, and (2) that supersymmetry protects infrared Lorentz invariance. A third scenario proposes that a classically Lorentz invariant matter sector with controlled quantum corrections may simply co-exist with Horava gravity under certain conditions. However, for non-projectable Horava gravity in 3+1 dimensions it is known that, in the absence of additional structures, this mechanism is spoiled by unexpected power-law divergences. We confirm this same result in the projectable version of the theory by employing the recently found gauge-fixing term that renders the shift and graviton propagators regular. We show that the problem persists for all dimensions $D\geq 3$, and that the degree of fine tuning in squared sound speeds between a U(1) gauge field and a scalar field increases with $D$. In particular, this difference in the zero external momentum limit is proportional to $\Lambda^{D-1}$ for $D\geq 3$, where $\Lambda$ is the ultraviolet momentum cutoff for loop integrals, while the power-law divergences are absent for $D=1$ and $D=2$. These results suggest that not only the gravity sector but also the matter sector should exhibit a transition to Lifshitz scaling above some scale, and that there should not be a large separation between the transition scales in the gravity and matter sectors. We close with a discussion of other more promising scenarios, including emergent Lorentz invariance from supersymmetry/strong dynamics, and pointing out challenges where they exist.

Ghosts in metric-affine higher order curvature gravity

We disprove the widespread belief that higher order curvature theories of gravity in the metric-affine formalism are generally ghost-free. This is clarified by considering a sub-class of theories constructed only with the Ricci tensor and showing that the non-projectively invariant sector propagates ghost-like degrees of freedom. We also explain how these pathologies can be avoided either by imposing a projective symmetry or additional constraints in the gravity sector. Our results put forward that higher order curvature gravity theories generally remain pathological in the metric-affine (and hybrid) formalisms and highlight the key importance of the projective symmetry and/or additional constraints for their physical viability and, by extension, of general metric-affine theories.

Enhanced di-Higgs signal from hidden scalar QCD at leading-order in the scale-symmetry limit

We develop an effective-model description arising from a recently proposed scale-invariant hidden scalar-QCD, which has been used to explain the dynamical origin of the electroweak scale. In addition to the previous works, our new effective model includes the dynamical scale-anomaly effect from the hidden QCD gluons, to explicitly break the classical-scale invariance at the level of an effective field theory, which is known as the leading-order scale-symmetry (LOSS). In the phenomenological analysis, the proposed model predicts a light composite dilaton composed of hidden scalar quarks and gluons with the mass around electroweak scale (around 280 GeV), and has only one input parameter, which is the mixing angle between the Higgs boson and the composite dilaton. Our result for the dilaton mass is in accord with the lattice simulation for scalar QCD, where the scalar-quark bound states acquire a large effective mass from the hidden gluon contribution. Furthermore, we predict several significant deviations from the SM, like the diHiggs production cross sections (maximally about 10 times larger than the SM prediction), that could be directly tested at the high luminosity LHC. It is also the first study for the diHiggs production signal predicted from a scale(conformal)-invariant hidden sector, even from dark/hidden QCD. Our proposed effective model is thus significantly different than the conventional realization of scale-invariant hidden-scalar QCD without the scale anomaly effect, and can potentially provide a competitive explanation for many exotic phenomena beyond the standard model, such as new dark matter candidates and a strongly first-order electroweak phase transition.