The deformed M2-brane

The superembedding formalism is used to study correction terms to the dynamics of the M2 brane in a flat background. This is done by deforming the standard embedding constraint. It is shown rigorously that the first such correction occurs at dimension four. Cohomological techniques are used to determine this correction explicitly. The action is derived to quadratic order in fermions, and the modified \k-symmetry transformations are given.Comment: 38 pages, 3 figure

Error Resilient Quantum Amplitude Estimation from Parallel Quantum Phase Estimation

We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude estimation, the parallelization can lead to vast improvements in resilience against quantum errors. The resilience is not caused by the lower gate depth, but by the structure of the algorithm. Even in cases with errors that make it impossible to read out the exact or approximate solutions from conventional amplitude estimation, our parallel approach provided the correct solution with high probability. The results on error resilience hold for the standard version and for low depth versions of quantum amplitude estimation. Methods presented are subject of a patent application [Quantum computing device: Patent application EP 21207022.1]

Kappa-symmetric deformations of M5-brane dynamics

We calculate the first supersymmetric and kappa-symmetric derivative deformation of the M5-brane worldvolume theory in a flat eleven-dimensional background. By applying cohomological techniques we obtain a deformation of the standard constraint of the superembedding formalism. The first possible deformation of the constraint and hence the equations of motion arises at cubic order in fields and fourth order in a fundamental length scale $l$. The deformation is unique up to this order. In particular this rules out any induced Einstein-Hilbert terms on the worldvolume. We explicitly calculate corrections to the equations of motion for the tensor gauge supermultiplet.Comment: 17 pages. Additional comments in section

Quantum amplitude estimation with error mitigation for time-evolving probabilistic networks

We present a method to model a discretized time evolution of probabilistic networks on gate-based quantum computers. We consider networks of nodes, where each node can be in one of two states: good or failed. In each time step, probabilities are assigned for each node to fail (switch from good to failed) or to recover (switch from failed to good). Furthermore, probabilities are assigned for failing nodes to trigger the failure of other, good nodes. Our method can evaluate arbitrary network topologies for any number of time steps. We can therefore model events such as cascaded failure and avalanche effects which are inherent to financial networks, payment and supply chain networks, power grids, telecommunication networks and others. Using quantum amplitude estimation techniques, we are able to estimate the probability of any configuration for any set of nodes over time. This allows us, for example, to determine the probability of the first node to be in the good state after the last time step, without the necessity to track intermediate states. We present the results of a low-depth quantum amplitude estimation on a simulator with a realistic noise model. We also present the results for running this example on the AQT quantum computer system PINE. Finally, we introduce an error model that allows us to improve the results from the simulator and from the experiments on the PINE system

The supermembrane revisited

The M2-brane is studied from the perspective of superembeddings. We review the derivation of the M2-brane dynamics and the supergravity constraints from the standard superembedding constraint and we discuss explicitly the induced d=3, N=8 superconformal geometry on the worldvolume. We show that the gauged supermembrane, for a target space with a U(1) isometry, is the standard D2-brane in a type IIA supergravity background. In particular, the D2-brane action, complete with the Dirac-Born-Infeld term, arises from the gauged Wess-Zumino worldvolume 4-form via the brane action principle. The discussion is extended to the massive D2-brane considered as a gauged supermembrane in a massive D=11 superspace background. Type IIA supergeometry is derived using Kaluza-Klein techniques in superspace.Comment: Latex, 46 pages, clarifying remarks and references adde

Kappa-symmetric Derivative Corrections to D-brane Dynamics

We show how the superembedding formalism can be applied to construct manifestly kappa-symmetric higher derivative corrections for the D9-brane. We also show that all correction terms appear at even powers of the fundamental length scale $l$. We explicitly construct the first potential correction, which corresponds to the kappa-symmetric version of the $\partial^4 F^4$, which one finds from the four-point amplitude of the open superstring.Comment: 20 pages. Minor changes, added reference

Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra

The effective action of D6-branes in N=1 type IIA orientifolds

We use a Kaluza-Klein reduction to compute the low-energy effective action for the massless modes of a spacetime-filling D6-brane wrapped on a special Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold. The modifications to the characteristic data of the N=1 bulk orientifold theory in the presence of a D6-brane are analysed by studying the underlying Type IIA supergravity coupled to the brane worldvolume in the democratic formulation and performing a detailed dualisation procedure. The N=1 chiral coordinates are found to be in agreement with expectations from mirror symmetry. We work out the Kahler potential for the chiral superfields as well as the gauge kinetic functions for the bulk and the brane gauge multiplets including the kinetic mixing between the two. The scalar potential resulting from the dualisation procedure can be formally interpreted in terms of a superpotential. Finally, the gauging of the Peccei-Quinn shift symmetries of the complex structure multiplets reproduces the D-term potential enforcing the calibration condition for special Lagrangian 3-cycles.Comment: 48 pages, v2: typos corrected, references adde

Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on T6/Z6'

The perturbative leading order open string three-point couplings for the Standard Model with hidden USp(6) on fractional D6-branes on T6/Z6' from arXiv:0806.3039 [hep-th], arXiv:0910.0843 [hep-th] are computed. Physical Yukawa couplings consisting of holomorphic Wilsonian superpotential terms times a non-holomorphic prefactor involving the corresponding classical open string Kaehler metrics are given, and mass terms for all non-chiral matter states are derived. The lepton Yukawa interactions are at leading order flavour diagonal, while the quark sector displays a more intricate pattern of mixings. While N=2 supersymmetric sectors acquire masses via only two D6-brane displacements - which also provide the hierarchies between up- and down-type Yukawas within one quark or lepton generation -, the remaining vector-like states receive masses via perturbative three-point couplings to some Standard Model singlet fields with vevs along flat directions. Couplings to the hidden sector and messengers for supersymmetry breaking are briefly discussed.Comment: 52 pages (including 8p. appendix); 5 figures; 14 tables; v2: discussion in section 4.1.3 extended, footnote 5 added, typos corrected, accepted by JHE

Supersymmetric Born-Infeld from the D9-brane

Using the superembedding approach, the full supersymmetric effective field theory of the D9-brane, super Born-Infeld theory, is fixed by the so called $\mathcal{F}$-constraint. The odd-odd components of the theory's super field strength, $f_{\alpha \beta}$, are implied by this constraint. Given $f_{\alpha \beta}$, the super Bianchi identities imply the theory's equations of motion. We calculate $f_{\alpha \beta}$ up to order 5 in fields, corresponding to order 6 in fields in the Lagrangian.Comment: 15 pages, references adde