Non-perturbative selection rules in F-theory

We discuss the structure of charged matter couplings in 4-dimensional F-theory compactifications. Charged matter is known to arise from M2-branes wrapping fibral curves on an elliptic or genus-one fibration Y. If a set of fibral curves satisfies a homological relation in the fibre homology, a coupling involving the states can arise without exponential volume suppression due to a splitting and joining of the M2-branes. If the fibral curves only sum to zero in the integral homology of the full fibration, no such coupling is possible. In this case an M2-instanton wrapping a 3-chain bounded by the fibral matter curves can induce a D-term which is volume suppressed. We elucidate the consequences of this pattern for the appearance of massive U(1) symmetries in F-theory and analyse the structure of discrete selection rules in the coupling sector. The weakly coupled analogue of said M2-instantons is worked out to be given by D1-F1 instantons. The generation of an exponentially suppressed F-term requires the formation of half-BPS bound states of M2 and M5-instantons. This effect and its description in terms of fluxed M5-instantons is discussed in a companion paper.Comment: 49 pages, 9 figures; v2: references adde

Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation

Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of low rate can be expanded into small shift errors. The qubit space is defined as an eigenspace of two mutually commuting displacement operators $S_p$ and $S_q$ which act as large shifts/translations in phase space. We propose and analyze the approximate creation of these qubit states by coupling the oscillator to a sequence of ancilla qubits. This preparation of the states uses the idea of phase estimation where the phase of the displacement operator, say $S_p$, is approximately determined. We consider several possible forms of phase estimation. We analyze the performance of repeated and adapative phase estimation as the simplest and experimentally most viable schemes given a realistic upper-limit on the number of photons in the oscillator. We propose a detailed physical implementation of this protocol using the dispersive coupling between a transmon ancilla qubit and a cavity mode in circuit-QED. We provide an estimate that in a current experimental set-up one can prepare a good code state from a squeezed vacuum state using $8$ rounds of adapative phase estimation, lasting in total about $4 \mu$ sec., with $94\%$ (heralded) chance of success.Comment: 24 pages, 15 figures. Some minor improvements to text and figures. Some of the numerical data has been replaced by more accurate simulations. The improved simulation shows that the code performs better than originally anticipate

Scale Economics, Market Power, and Pricing Behavior Evidence from German Newspaper and Magazine Publishing

The anomalous inverse concentration-price relationship observed by some researchers in the newspaper market has been attributed to scale economies. In this paper we suggest that the newspaper's (or magazine's) "double-product" feature (i.e., news supplied to readers and advertising space supplied to advertisers) is the main source of this anomaly. In a simple oligopoly model it is shown how a profit-maximizing publisher takes advantage of that feature. Empirically an inverse concentration-price relationship may arise if double-product pricing is not controlled for. Regression results for a cross-section of 222 German Newspapers and magazines corroborate the theoretical implications.Scale Economics, Advertising, Concentration, Pricing Behavior

Heterotic Vacua from general (non-) Abelian Bundles

We report on the construction of four-dimensional string vacua by considering general abelian and non-abelian bundles on an internal Calabi-Yau for both heterotic theories. The structure of the resulting gauge sector is extremely rich and gives rise to many new model building possibilities. We analyse the chiral spectrum including the contribution from heterotic five-branes and provide the general consistency conditions. The one-loop corrected supersymmetry condition on the bundles is found to be that of pi-stability. As an application we present a supersymmetric Standard-Model like example for the SO(32) string with U(n) bundles on an elliptically fibered Calabi-Yau.Comment: 8 pages; Contribution to the proceedings of the RTN network conference "Constituents, Fundamental Forces and Symmetries of the Universe" in Corfu, Greece, 20-26 September 2005; v2: typo in equation (11) corrected and one footnote adde

Algebraic Cycles and Local Anomalies in F-Theory

We introduce a set of identities in the cohomology ring of elliptic fibrations which are equivalent to the cancellation of gauge and mixed gauge-gravitational anomalies in F-theory compactifications to four and six dimensions. The identities consist in (co)homological relations between complex codimension-two cycles. The same set of relations, once evaluated on elliptic Calabi-Yau three-folds and four-folds, is shown to universally govern the structure of anomalies and their Green-Schwarz cancellation in six- and four-dimensional F-theory vacua, respectively. We furthermore conjecture that these relations hold not only within the cohomology ring, but even at the level of the Chow ring, i.e. as relations among codimension-two cycles modulo rational equivalence. We verify this conjecture in non-trivial examples with Abelian and non-Abelian gauge groups factors. Apart from governing the structure of local anomalies, the identities in the Chow ring relate different types of gauge backgrounds on elliptically fibred Calabi-Yau four-folds.Comment: 45 page

Heterotic GUT and Standard Model Vacua from simply connected Calabi-Yau Manifolds

We consider four-dimensional supersymmetric compactifications of the E8 x E8 heterotic string on Calabi-Yau manifolds endowed with vector bundles with structure group SU(N) x U(1) and five-branes. After evaluating the Green-Schwarz mechanism and deriving the generalized Donaldson-Uhlenbeck-Yau condition including the five-brane moduli, we show that this construction can give rise to GUT models containing U(1) factors like flipped SU(5) or directly the Standard Model even on simply connected Calabi-Yau manifolds. Concrete realizations of three-generation models on elliptically fibered Calabi-Yau manifolds are presented. They exhibit the most attractive features of flipped SU(5) models such as doublet-triplet splitting and proton stability. In contrast to conventional GUT string models, the tree level relations among the Standard Model gauge couplings at the GUT scale are changed.Comment: 46 pages, 2 figures, 6 tables; v2: references added, typos corrected; v3: typos corrected, final version published in Nucl.Phys.