Duality Constraints Research Articles

Optimizing local electricity markets: A bi-level primal-dual approach for integrating price-based demand response and distribution locational marginal pricing

This paper addresses the conundrum of optimizing electricity consumption patterns in response to fluctuations in demand and price, a task managed by both load aggregators and the distribution system operator (DSO). The conventional approaches in the literature to integrate demand response (DR) into optimal power flow (OPF) problems typically overlook the price responsiveness of consumers or simplify power flow equations to account for price-elastic demand.In this paper, we strive to close this gap by introducing a bi-level primal-dual optimization framework that incorporates aggregators' objectives into the market-clearing process while preserving the precision of the OPF equations. At the upper level, the model seeks to minimize both the total payment and peak load. The lower level, structured as a second-order conic (SOC) problem, aims to reduce overall generation costs subject to constraints of the second-order conic (SOC) branch flow model (BFM). The two levels interact through the optimal demand response and distribution locational marginal prices (DLMPs). The principles of convex duality principles together with the strong duality constraint are leveraged to transform the market-clearing problem into a single primal-dual problem. We also circumvent the non-linearity that stems from the DR payment term by incorporating discretizing loads and the big-M method, thus converting the problem into a mixed-integer SOC (MI-SOC) formulation. The merits of the proposed MI-SOC framework are validated through case studies conducted on the IEEE 33-bus test system, showcasing its potential to enforce price-elasticity demand response in distribution system's electricity markets.

Momentum Shell in Quarkyonic Matter from Explicit Duality: A Dual Model for Cold, Dense QCD.

We present a model of cold QCD matter that bridges nuclear and quark matter through the duality relation between quarks and baryons. The baryon number and energy densities are expressed as functionals of either the baryon momentum distribution, f_{B}, or the quark distribution, f_{Q}, which are subject to the constraints on fermions, 0≤f_{B,Q}≤1. The theory is ideal in the sense that the confinement of quarks into baryons is reflected in the duality relation between f_{Q} and f_{B}, while other possible interactions among quarks and baryons are all neglected. The variational problem with the duality constraints is formulated and we explicitly construct analytic solutions, finding two distinct regimes: a nuclear matter regime at low density and a quarkyonic regime at high density. In the quarkyonic regime, baryons underoccupy states at low momenta but form a momentum shell with f_{B}=1 on top of a quark Fermi sea. Such a theory describes a rapid transition from a soft nuclear equation of state to a stiff quarkyonic equation of state. At this transition, there is a rapid increase in the pressure.

Simple bulk reconstruction in anti-de Sitter/conformal field theory correspondence

Abstract In this paper, we show that bulk reconstruction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is rather simple and has an intuitive picture, by showing that the HKLL (Hamilton-Kabat-Lifschytz-Lowe) bulk reconstruction formula can be simplified. We also reconstruct the wave packets in the bulk theory from the CFT primary operators. With these wave packets, we discuss the causality and duality constraints and find our picture is the only consistent one. Our picture of the bulk reconstruction can be applied to the asymptotic AdS spacetime.

On the positivity of Coon amplitude in D = 4

The Coon amplitude is the unique solution to duality constraints with logarithmic Regge trajectories. A striking feature of this solution is that it interpolates between the Veneziano amplitude and a scalar particle amplitude. However, an analytic proof of unitarity of the amplitude is not yet known. In this short note, we explicitly compute the partial wave coefficients on the leading Regge trajectory in D = 4. We find that these coefficients always remain positive, even though their magnitude decreases with spin. Since the coefficients on the subleading trajectories are observed to be larger than those on the leading ones, our result indicates the positivity of the full Coon amplitude in D = 4.

Unitarity and Low Energy Expansion of the Coon Amplitude.

The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this Letter, we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switches from a regime where it is positive in all dimensions to a regime with critical dimensions, which connects to the known d=26, 10 when the deformation is removed. Incidentally, we find that the Veneziano amplitude can be extended to massive scalars of masses up to m^{2}=1/3, where it has critical dimension 6.3. On the low-energy side, we compute the first few couplings of the theory in terms of q-deformed analogs of the standard Riemann zeta values of the string expansion. We locate their location in the EFT-hedron, and find agreement with a recent conjecture that theories with accumulation points populate this space. We also discuss their relation to low spin dominance. Finally, we comment on the length of the Coon parton.

An improved holographic nodal line semimetal

We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators overline{psi}{gamma}^{mu v}psi and overline{psi}{gamma}^{mu v}{gamma}^5psi . We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spectrum which are topologically nontrivial. The bulk geometries are different from the previous model without the duality constraint, while the resulting properties are qualitatively similar to those in that model. This improved model provides a more natural ground to analyze transports or other properties of strongly coupled nodal line semimetals.

Toward exotic 6D supergravities

We investigate exotic supergravity theories in 6D with maximal (4,0) and (3,1) supersymmetry, which were conjectured by C. Hull to exist and to describe strong coupling limits of ${\cal N}=8$ theories in 5D. These theories involve exotic gauge fields with non-standard Young tableaux representations, subject to (self-)duality constraints. We give novel actions in a 5+1 split of coordinates whose field equations reproduce those of the free bosonic (4,0) and (3,1) theory, respectively, including the (self-)duality relations. Evidence is presented for a master exceptional field theory formulation with an extended section constraint that, depending on the solution, produces the (4,0), (3,1) or the conventional (2,2) theory. We comment on the possible construction of a fully non-linear master exceptional field theory.

Duality and supersymmetry constraints on the weak gravity conjecture

Positivity bounds coming from consistency of UV scattering amplitudes are not always sufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved SL(2, ℝ) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved O(d, d; ℝ) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states.

Surface terms in the effective actions via duality constraints

The effective action of string theory on a spacetime manifold with boundary has both bulk and boundary terms. We propose that both bulk and boundary actions, may be found by imposing the effective action to be invariant under the gauge transformations and under the string dualities. Using this proposal at the leading order of α′, the standard Gibbons-Hawking-York boundary term is reproduced.

Duality and axionic weak gravity

The axionic weak gravity conjecture predicts the existence of instantons whose actions are less than their charges in appropriate units. We show that the conjecture is satisfied for the axion-dilaton-gravity system if we assume duality constraints on the higher derivative corrections in addition to positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. On the other hand, the conjecture does not follow if we assume the positivity bounds only. This presents an example where derivation of the weak gravity conjecture requires more detailed UV information than the consistency of scattering amplitudes.

Unitarity, analyticity and duality constraints in η and π photoproduction

We report an update of the isobar model EtaMAID. A new approach is proposed to avoid double counting in the overlap region of Regge and resonances. Dispersion relation is applied on top of the isobar model, and both models describe the data equally well. Application of these ideas to pion photoproduction is discussed.

Duality Constraints on Counterterms in Supergravities

AbstractThe UV finiteness found in calculations of the 4‐point amplitude in supergravity at loop order has not been explained, which motivates our study of the relevant superspace invariants and on‐shell superamplitudes for both and . The local 4‐point superinvariants for are expected to have nonlinear completions whose 6‐point amplitudes have non‐vanishing SSL's (soft scalar limits), violating the behavior required of Goldstone bosons. For , we find at that local 6‐point superinvariant and superamplitudes, which might cancel these SSL's, do not exist. This rules out the candidate 4‐point counterterm and thus gives a plausible explanation of the observed finiteness. However, at we construct a local 6‐point superinvariant with non‐vanishing SSL's, so the SSL argument does not explain the observed UV finiteness. For supergravity there are no 6‐point invariants at either or 4, so the SSL argument predicts UV finiteness.

Holographic dark energy from fluid/gravity duality constraint by cosmological observations

In this paper, we obtain a holographic model of dark energy using the fluid/gravity duality. This model will be dual to a higher dimensional Schwarzschild black hole, and we would use fluid/gravity duality to relate to the parameters of this black hole to such a cosmological model. We will also analyze the thermodynamics of such a solution, and discuss the stability model. Finally, we use cosmological data to constraint the parametric space of this dark energy model. Thus, we will use observational data to perform cosmography for this holographic model based on fluid/gravity duality.

Multiparty Session Types, Beyond Duality (Abstract)

Multiparty Session Types (MPST) are a well-established typing discipline for message-passing processes interacting on sessions involving two or more participants. Session typing can ensure desirable properties: absence of communication errors and deadlocks, and protocol conformance. However, existing MPST works provide a subject reduction result that is arguably (and sometimes, surprisingly) restrictive: it only holds for typing contexts with strong duality constraints on the interactions between pairs of participants. Consequently, many "intuitively correct" examples cannot be typed and/or cannot be proved type-safe. We illustrate some of these examples, and discuss the reason for these limitations. Then, we outline a novel MPST typing system that removes these restrictions.

Exotic dual of type II double field theory

We perform an exotic dualization of the Ramond–Ramond fields in type II double field theory, in which they are encoded in a Majorana–Weyl spinor of O(D,D). Starting from a first-order master action, the dual theory in terms of a tensor–spinor of O(D,D) is determined. This tensor–spinor is subject to an exotic version of the (self-)duality constraint needed for a democratic formulation. We show that in components, reducing O(D,D) to GL(D), one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, such as the 4-form in type IIB string theory.

Double-copy constructions and unitarity cuts

The duality between color and kinematics enables the construction of multiloop gravity integrands directly from corresponding gauge-theory integrands. This has led to new nontrivial insights into the structure of gravity theories, including the discovery of enhanced ultraviolet cancellations. To continue to gain deeper understandings and probe these new properties, it is crucial to further improve techniques for constructing multiloop gravity integrands. In this paper, we show by example how one can alleviate difficulties encountered at the multiloop level by relaxing the color-kinematics duality conditions to hold manifestly only on unitarity cuts instead of globally on loop integrands. As an example, we use a minimal ansatz to construct an integrand for the two-loop four-point nonsupersymmetric pure Yang-Mills amplitude in $D$ dimensions that is compatible with these relaxed color-kinematics duality constraints. We then immediately obtain a corresponding gravity integrand through the double-copy procedure. Comments on ultraviolet divergences are also included.

Quark–hadron duality constraints on γZ box corrections to parity-violating elastic scattering

We examine the interference γZ box corrections to parity-violating elastic electron–proton scattering in the light of the recent observation of quark–hadron duality in parity-violating deep-inelastic scattering from the deuteron, and the approximate isospin independence of duality in the electromagnetic nucleon structure functions down to Q2≈1 GeV2. Assuming that a similar behavior also holds for the γZ proton structure functions, we find that duality constrains the γZ box correction to the proton's weak charge to be ℜe□γZV=(5.4±0.4)×10−3 at the kinematics of the Qweak experiment. Within the same model we also provide estimates of the γZ corrections for future parity-violating experiments, such as MOLLER at Jefferson Lab and MESA at Mainz.

Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds

The 6d effective action of F-theory compactified on an elliptically fibred CalabiYau threefold is determined using an M-theory lift. The non-Abelian gauge theory arises on a stack of seven-branes located on the singularities of the threefold. The gauge theory is analysed in the 5d Coulomb branch by resolving the Calabi-Yau threefold. The reduction includes an arbitrary number of 6d tensor multiplets for which the self- and anti-self duality constraints can be imposed in the 5d M-theory set-up. Higher curvature terms are crucial for anomaly cancellation in six dimensions, and are obtained from corrections to the 11d supergravity action. The chiral spectrum in a 6d supergravity theory is linked to the form of the Green-Schwarz couplings via anomalies. We find that these data are encoded in the 5d effective action via one loop corrections.

Test of Universal Rise of Hadronic Total Cross Sections Based on πp, Kp, \-pp and pp Scatterings

Abstract There are several evidences of the hadronic total cross section σtot to be proportional to B log2s consistent with the Froissart unitarity bound. The COMPETE collaboration has further assumed σtot ≃ B log2(s/s0) + Z to extend its universal rise with the common value of B for all hadronic scatterings to reduce the number of adjustable parameters. The coefficient B is suggested to be universal in the arguments of color glass condensate (CGC) of QCD. There has been, however, no rigorous proof yet based only on QCD. We attempt to investigate the values of B for πxxxp, Kxxxp and p¯p, pp scatterings respectively through the search for the simultaneous best fit to the experimental σtot and ρ ratios at high energies. The σtot at the resonance and intermediate energy regions has also been exploited as a duality constraint based on the special form of finite-energy sum rule (FESR). We estimate the values of B individually for πxxxp, Kxxxp and p¯p, pp scatterings without using the universality hypothesis. It turs out that the values of B are mutually consistent within one standard deviation, and the universal rise of hadronic total cross sections is strongly suggested. It has to be stressed that we cannot obtain such a definite conclusion without the duality constraint.

Stringy KLT relations, global symmetries, and E 7(7)-violation

We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to tree amplitudes in toroidal compactifications of string theory to four dimensions. The closed string tree amplitudes with massless external states respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8) R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses on two aspects: (i) We provide a detailed account of the simplest SU(8)-violating amplitudes. We classify these processes and derive explicit superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4) symmetry at order alpha'^3. Their origin is the dilatonic operator exp(-6 phi) R^4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order alpha'^3 and use two different methods to isolate the SU(8)-singlet contribution from exp(-6 phi) R^4. This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R^4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N=8 supergravity candidate counterterm R^4 is incompatible with continuous E_7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R^4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.