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We study $ \text{T}\overline{\text{T}} $ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $ \text{T}\overline{\text{T}} $-deformed Lagrangian can be computed in closed form, giving rise to a novel non-local action in Sen's formalism. We establish that at the limit of infinite $ \text{T}\overline{\text{T}} $ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $ \text{T}\overline{\text{T}} $-deformed chiral fermions, and point out that the stress tensor of the $ \text{T}\overline{\text{T}} $-deformed free fermion coincides with the undeformed seed theory. We explain this behaviour of the stress tensor by noting that the deformation term in the action is purely topological in nature and closely resembles the fermionic Wess-Zumino term in the Green-Schwarz formalism. In turn, this observation also explains a puzzle in the literature, viz. why the $ \text{T}\overline{\text{T}} $ deformation of multiple free fermions truncate at linear order. We conclude by discussing the possibility of an interplay between $ \text{T}\overline{\text{T}} $ deformations and bosonisation., v2: 26 pages. Substantial changes in Sections 4 and 5. Abstract updated, typos corrected, references and acknowledgement added

We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group. Under the impact of quantum gravity, a finite value of the gauge coupling could be generated and in turn drive four-fermion interactions to criticality. We find indications that the gravity-gauge-fermion interplay protects the lightness of fermions for a large enough number of fermions. On the other hand, for a smaller number of fermions, chiral symmetry may be broken, which would be in tension with the observation of light fermions., 12 pages, 6 figures. Match the published version

In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a 't Hooft anomaly. In practice, preserving a symmetry that is realised on fermions in a chiral manner necessitates some dynamics beyond simple quadratic mass terms. We show how this can be achieved using familiar results about supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4d fermions that carry the quantum numbers of one generation of the Standard Model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly., 21 pages. v2: references added

We derive the entanglement entropy of chiral fermions on the circle at arbitrary temperature. The spin-sector contribution depends only on the total length of the entangling region, regardless of the configuration of the intervals. Thus three-partite information provides a global indicator for the spin boundary conditions. Together with the modular Hamiltonian, our results provide a systematic way of obtaining relative entropy on the torus., Comment: 8 pages, 2 figures; corrected error in section C, some improvements to the exposition

We consider a lattice implementation of the eta-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating five-dimensional gauge field. We clarify the relation to the effective action for chiral Ginsparg-Wilson fermions. The integrability, which holds true for anomaly-free theories in the classical continuum limit, is not assured on the lattice with a finite spacing. A lattice expression for the five-dimensional Chern-Simons term is obtained., Comment: 38 pages, LaTeX, revised version

We study renormalization group flows in strongly interacting field theories with fermions that correspond to transitions between a theory without Lorentz invariance at high energies down to a theory with approximate Lorentz symmetry in the infrared. Holographic description of the strong coupling is used. The emphasis is made on emergence of chiral fermions in the low-energy theory., Comment: 28 pages, 2 figures

We determine the reduced density matrix of chiral fermions on the torus, for an arbitrary set of disjoint intervals and generic torus modulus. We find the resolvent, which yields the modular Hamiltonian in each spin sector. Together with a local term, it involves an infinite series of bi-local couplings, even for a single interval. These accumulate near the endpoints, where they become increasingly redshifted. Remarkably, in the presence of a zero mode, this set of points 'condenses' within the interval at low temperatures, yielding continuous non-locality., Comment: Several minor changes done in order to improve readability. Accepted for publication in PRL

The Standard Models contain chiral fermions coupled to gauge theories. It has been a long-standing problem to give such gauged chiral fermion theories a quantum non-perturbative definition. By classification of quantum anomalies and symmetric invertible topological orders via a mathematical cobordism theorem for differentiable and triangulable manifolds, and the existence of symmetric gapped boundary for the trivial symmetric invertible topological orders, we propose that Spin(10) chiral fermion theories with Weyl fermions in 16-dimensional spinor representations can be defined on a 3+1D lattice, and subsequently dynamically gauged to be a Spin(10) chiral gauge theory. As a result, the Standard Models from the 16n-chiral fermion SO(10) Grand Unification can be defined non-perturbatively via a 3+1D local lattice model of bosons or qubits. Furthermore, we propose that Standard Models from the 15n-chiral fermion SU(5) Grand Unification can also be realized by a 3+1D local lattice model of fermions., 24 pages. Two columns. v3: Refinement with detailed discussions. Appendices include viewpoints from perturbative local anomalies and non-perturbative global anomalies (e.g. arXiv:1810.00844, SU(2) = Spin(3) $\subset$ Spin(10)), and co/bordism theories (e.g. $\Omega_{D}^{{(\mathrm{Spin}(D) \times \mathrm{Spin}(10))}/{\mathbb{Z}_2^f}}$)

In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT) background, using a Schwinger-DeWitt heat kernel technique, we compute non-perturbatively the two (odd parity) trace anomalies. A suitable collapsing limit of this model corresponds to a theory of chiral fermions coupled to (ordinary) gravity. Taking this limit on the two computed trace anomalies we verify that they tend to the same expression, which coincides with the already found odd parity trace anomaly, with the identical coefficient. This confirms our previous results on this issue., Comment: 43 pages, some additions in section 6.3 and 6.5 plus minor corrections

Disordered 2D chiral fermions provide an effective description of several materials including graphene and topological insulators. While previous analysis considered delta correlated disorder and no ultraviolet cut-offs, we consider here the effect of short range correlated disorder and the presence of a momentum cut-off, providing a more realistic description of condensed matter models. We show that the density of states is anomalous with a critical exponent function of the disorder and that conductivity is universal only when the ultraviolet cut-off is removed, as consequence of the supersymmetric cancellation of the anomalies.

We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa's method supplemented by the choice of a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise., 25 pages, added references and acknowledgments

We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions., 14 pages, 9 figures

We show that a hot rotating fluid of relativistic chiral fermions possesses a new gapless collective mode associated with coherent propagation of energy density and chiral density waves along the axis of rotation. This mode, which we call the Chiral Heat Wave, emerges due to a mixed gauge-gravitational anomaly. At finite density the Chiral Heat Wave couples to the Chiral Vortical Wave while in the presence of an external magnetic field it mixes with the Chiral Magnetic Wave. The coupling of the Chiral Magnetic and Chiral Vortical Waves is also demonstrated. We find that the coupled waves - which are coherent fluctuations of the vector, axial and energy currents - have generally different velocities compared to the velocities of the individual waves., 33 pages, 6 figures; v2: minor changes, published version

We study the non-dissipative transport effects appearing at second order in the hydrodynamic expansion for a non-interacting gas of chiral fermions by using the partition function formalism. We discuss some features of the corresponding constitutive relations, derive the explicit expressions for the conductivities and compare with existing results in the literature., Comment: 9 pages. Talk given by E.Megias at the 4th International Conference on New Frontiers in Physics (ICNFP 2015), 23-30 August 2015, Kolymbari, Crete, Greece

The coadjoint orbit method is applied to the construction of Hamiltonian dynamics of massless particles of arbitrary helicity. The unusual transformation properties of canonical variables are interpreted in terms of nonlinear realizations of Poincare group. The action principle is formulated in terms of new space-time variables with standard transformation properties., Comment: 26 opages; no figures; few references added

We provide a pedagogical introduction to a recently studied class of phenomenologically interesting string models, known as Intersecting D-Brane Models. The gauge fields of the Standard-Model are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersections can give rise to chiral fermions. We address the basic issues and also provide an overview of the recent activity in this field. This article is intended to serve non-experts with explanations of the fundamental aspects, and also to provide some orientation for both experts and non-experts in this active field of string phenomenology., Comment: 85 pages, 8 figures, Latex, Bibtex, v2: refs added, typos corrected

We review the construction of chiral four-dimensional compactifications of type IIA string theory with intersecting D6-branes. Such models lead to four-dimensional theories with non-abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to building of models with spectrum as close as possible to the Standard Model, and review their main phenomenological properties. We also emphasize the advantages/disadvantages of carrying out this idea using supersymmetric of non-supersymmetric models., 30 pages, 16 figures, contribution to the proceedings of the TMR meeting `The quantum structure of spacetime', Leuven, September 2002

We define chiral fermions in the presence of non-trivial gravitational and gauge background fields in the framework of locally covariant field theory. This allows to straightforwardly compute the chiral anomalies on non-compact Lorentzian space-times, without recourse to a weak field approximation., Comment: 19 pages

We compute the partition function for non-interacting chiral fermions at second order in a derivative expansion of an arbitrary time-independent gravitational and gauge background. We find that Pauli-Villars regularization of the vacuum part is needed to get consistent results. We use our results to discuss some features of the non-dissipative constitutive relations of second order hydrodynamics., 27 pages; v2 minor changes in sec. 5 and discussion improved in secs. 6 and 7, references added, version to appear in JHEP

Comparing recent lattice results on chiral fermions and old continuum results for the index puzzling questions arise. To clarify this issue we start with a critical reconsideration of the results on finite lattices. We then work out various aspects of the continuum limit. After determining bounds and norm convergences we obtain the limit of the anomaly term. Collecting our results the index relation of the quantized theory gets established. We then compare in detail with the Atiyah-Singer theorem. Finally we analyze conventional continuum approaches., Comment: 34 pages; a more detaild introduction and a subsection with remarks on literature added

The progress brought to the study of chiral fermions and gauge theories by quantization methods with a bulk time suggests their usefulness in supersymmetric theories. Using superspace methods, we show how an explicitly supersymmetric version of such quantization methods may be given., 6 pages

We present what we believe is the minimal three-family $AdS/CFT$ model compactified on a nonabelian orbifold $S^{5}/(Q\times Z_{3})$. Nontrivial irreps of the discrete nonabelian group $Q\times Z_{3}$ are identified with the $4$ of $SU(4)$ $R$ symmetry to break all supersymmetries, and the scalar content of the model is sufficient to break the gauge symmetry to the standard model. According to the conformality hypothesis the progenitor $SU(4)^3 \times SU(2)^{12}$ theory becomes conformally invariant at an infra-red fixed point of the renormalization group., 11 pages latex and one JPG figure

We study localization of bulk fermions on a brane with inclusion of Yang-Mills and scalar backgrounds in higher dimensions and give the conditions under which localized chiral fermions can be obtained., Comment: Latex, 5 pages. A factor "2" mistake that propagated through a number of equations is corrected. Conclusions unchanged

An interesting tool for investigating the quantum features of a field theory is the introduction of compensating fields. For instance, the anomalous divergence of the chiral current can be calculated in the field-antifield formalism from an extended form of QCD with compensating fields. The interpretation of this procedure from the bosonized point of view, in the two dimensional case, crucially depends on the possibility of defining a bosonized version for the extended theory. We show, by using some recent results on the soldering of bosonized actions corresponding to chiral fermions, how is the mapping between bosonic and fermionic representations of this extended $QCD_2$. In the bosonic formulation the anomalous divergence of the chiral current shows up from the equations of motion of the compensating fields., Comment: Problems in the data transfer corrected; 16 pages, Latex, no figures

Motivated by the search for possible CP violating terms in the trace of the energy-momentum tensor in theories coupled to gravity we revisit the problem of trace anomalies in chiral theories. We recalculate the latter and ascertain that in the trace of the energy-momentum tensor of theories with chiral fermions at one-loop the Pontryagin density appears with an imaginary coefficient. We argue that this may break unitarity, in which case the trace anomaly has to be used as a selective criterion for theories, analogous to the chiral anomalies in gauge theories. We analyze some remarkable consequences of this fact, that seem to have been overlooked in the literature., 16 pages; v2: added 2 references in a footnote; v3: a few typos corrected, published in JHEP

Combining the Kaplan surface mode approach for chiral fermions with added terms motivated by Eichten and Preskill suggests the possibility for a lattice regularization of the standard model which is finite, exactly gauge invariant, and only has physically desired states in its low energy spectrum. The conjectured scheme manifestly requires anomaly cancelation and explicitly contains baryon and lepton number violating terms., 11 pages, latex

We introduce an index indicating the occurrence of chiral fermions at the inter- section of branes in matrix models. This allows to discuss the stability of chiral fermions under perturbations of the branes.

An off-shell manifestly (8,0) worldsheet supersymmetric formulation of a multiplet describing physical chiral fermions is given. The multiplet can be used to complete the doubly supersymmetric (twistor-like) action for the heterotic string. Correction of technical errors., 10 pages

We investigate the possibility of coupling a chemical potential only to the physical chiral fermions on the lattice starting from the many body state description of overlap fermions. After developing the formalism for a chiral gauge theory, we focus our attention on the case of free fermions coupled to a vector like chemical potential and discuss the issue of zero temperature divergences., 17 pages, 3 figures, minor changes to v1, version to appear in JHEP

We suggest a thick braneworld model in the squared curvature gravity theory. Despite the appearance of higher order derivatives, the localization of gravity and various bulk matter fields is shown to be possible. The existence of the normalizable gravitational zero mode indicates that our four-dimensional gravity is reproduced. In order to localize the chiral fermions on the brane, two types of coupling between the fermions and the brane forming scalar is introduced. The first coupling leads us to a Schr\"odinger equation with a volcano potential, and the other a P\"oschl-Teller potential. In both cases, the zero mode exists only for the left-hand fermions. Several massive KK states of the fermions can be trapped on the brane, either as resonant states or as bound states., Comment: 18 pages, 5 figures and 1 table, references added, improved version to be published in JHEP

We analyze quantization of noncommutative chiral electrodynamics in the enveloping algebra formalism in linear order in noncommutativity parameter $\theta$. Calculations show that divergences exist and cannot be removed by ordinary renormalization, however they can be removed by the Seiberg-Witten redefinition of fields. Performing the redefinitions explicitly, we obtain renormalizable lagrangian and discuss the influence of noncommutativity on field propagation. Noncommutativity affects the propagation of chiral fermions only: half of the fermionic modes become massive and birefringent., Comment: 16 pages, Version published in Phys. Rev. D

We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills-Higgs-Dirac theories with dynamical mass generation and exactly massless chiral fermions., Comment: 10 pages; Based on invited talk given by the first author at the 2nd School on "Quantum Gravity and Quantum Geometry" session of the 9th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, September 13-20 2009. To be published in General Relativity and Gravitation

Thermal leptogenesis explains the observed matter-antimatter asymmetry of the universe in terms of neutrino masses, consistent with neutrino oscillation experiments. We present a full quantum mechanical calculation of the generated lepton asymmetry based on Kadanoff-Baym equations. Origin of the asymmetry is the departure from equilibrium of the statistical propagator of the heavy Majorana neutrino, together with CP violating couplings. The lepton asymmetry is calculated directly in terms of Green's functions without referring to "number densities". Compared to Boltzmann and quantum Boltzmann equations, the crucial difference are memory effects, rapid oscillations much faster than the heavy neutrino equilibration time. These oscillations strongly suppress the generated lepton asymmetry, unless the standard model gauge interactions, which cause thermal damping, are properly taken into account. We find that these damping effects essentially compensate the enhancement due to quantum statistical factors, so that finally the conventional Boltzmann equations again provide rather accurate predictions for the lepton asymmetry., 57 pages, 11 figures; published version including erratum concerning Boltzmann limit for zero thermal widths

Torsion arising from fermionic matter in the Einstein-Cartan formulation of general relativity is considered in the context of Robertson-Walker geometries and the early Universe. An ambiguity in the way torsion arising from hot fermionic matter in chiral models should be implemented is highlighted and discussed. In one interpretation, chemical potentials in chiral models can contribute to the Friedmann equation and give a negative contribution to the energy density., 5 pages revtex4; error in v1 corrected.

The current flow from the bulk is due to the anomaly on the brane-but the absence of current flow is not, necessarily, due to anomaly cancellation, but to the absence of the chiral zero modes themselves, due to the existence of the layered phase. This can be understood in terms of the difference between the Chern-Simons terms in three and five dimensions. Thus the anomaly cancellation in four dimensions, which is essential for shielding the boundary from quantum effects within the bulk, makes sense only along the transition line between the layered and the Coulomb phase, which, in turn, requires the presence of a compact U(1) factor for the gauge group., Comment: 6 pages, 4 figures, LaTeX2e, uses PoS. Contribution to The XXVII International Symposium on Lattice Field Theory - LAT2009, July 26-31 2009,Peking University, Beijing, China

We propose a reduced form of Atiah-Patodi-Singer spectral boundary conditions for odd ($d$) dimensional spatial bag evolving in even ($d+1$) dimensional space-time. The modified boundary conditions are manifestly chirally invariant and do not depend on time. This allows to apply Hamiltonian approach to confined massless fermions and study chirality effects in spatially closed volume. The modified boundary conditions are equally suitable for chiral fermions in Minkowski and Euclidean metric space-times., Talk given at Seventh Workshop on Quantum Field Theory under the Influence of External Conditions, QFEXT'05, Barcelona, September 2005

We consider the (2, 0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. The naive invariance of the model under such transformations is however explicitly broken by anomalies: The electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet suffers from a classical anomaly, and there is also a one-loop quantum anomaly from the chiral fermions on the string world-sheet. Both of these contributions are proportional to the Euler class of the normal bundle of the string world-sheet, and consistency of the model requires that they cancel. This imposes strong constraints on possible models, which are found to obey an ADE-classification. We then consider the decoupled world-sheet theory that describes low-energy fluctuations (compared to the scale set by the string tension) around a configuration with a static, straight string. The anomaly structure determines this to be a supersymmetric version of the level one Wess-Zumino-Witten model based on the group (R x SU(2))/Z_2 ., Comment: 14 pages. Further clarifications and references added

We present an exactly soluble charged wormhole model in two dimensions by adding infalling chiral fermions on the static wormhole. The infalling energy due to the infalling charged matter requires the classical back reaction of the geometry, which is solved by taking into account of the nontrivial nonchiral exotic energy. Finally, we obtain the exact expression for the size of the throat depending on the total amount of the infalling net energy and discuss the interesting transition from the AdS spacetime to the wormhole geometry., Comment: 8 pages, no figures

We study chiral symmetries of fermionic non commutative dipole theories. By using Fujikawa's approach we obtain explicit expressions of the anomalies for Dirac and chiral fermions in 2 and 4 dimensions., Comment: 11pages, latex file. Comments added

We clarify RR tadpole cancellation conditions for intersecting D4-/D5-branes. We find all of the D4-brane models which have D=4 three-generation chiral fermions with the SU(3)XSU(2)XU(1)^n symmetries. For the D5-brane case, we present a solution to the conditions which gives exactly the matter contents of standard model with U(1) anomalies., 6 pages, submitted to Progress Letters

A systematic analysis is presented of compactifications of the IIB superstring on $AdS_5 \times S^5/\Gamma$ where $\Gamma$ is a non-abelian discrete group. Every possible $\Gamma$ with order $g \leq 31$ is considered. There exist 45 such groups but a majority cannot yield chiral fermions due to a certain theorem that is proved. The lowest order to embrace the nonSUSY standard $SU(3) \times SU(2) \times U(1)$ model with three chiral families is $\Gamma = D_4 \times Z_3$, with $g=24$; this is the only successful model found in the search. The consequent uniqueness of the successful model arises primarily from the scalar sector, prescribed by the construction, being sufficient to allow the correct symmetry breakdown., Comment: 121 pages (sorry) LATEX and one JPG figure

We present an explicit formulation of supersymmetric Yang-Mills theories from $\D=$ 5 to 10 dimensions in the familiar $\N=1,\D=4$ superspace. This provides the rules for globally supersymmetric model building with extra dimensions and in particular allows us to simply write down $\N=1$ SUSY preserving interactions between bulk fields and fields localized on branes. We present a few applications of the formalism by way of illustration, including supersymmetric ``shining'' of bulk fields, orbifolds and localization of chiral fermions, anomaly inflow and super-Chern-Simons theories., Comment: Typos corrected. Added reference to early work by Marcus, Sagnotti and Siegel and a term to the non-Abelian Lagrangian for D>5 formally needed for gauge invariance. The results however remain unchanged

Intersecting Dp-branes often give rise to chiral fermions living on their intersections. We study the construction of four-dimensional chiral gauge theories by considering configurations of type II D(3+n)-branes wrapped on non-trivial n-cycles on T^{2n} x(R^{2(3-n)}/Z_N), for n=1,2,3. The gauge theories on the four non-compact dimensions of the brane world-volume are generically chiral and non-supersymmetric. We analyze consistency conditions (RR tadpole cancellation) for these models, and their relation to four-dimensional anomaly cancellation. Cancellation of U(1) gauge anomalies involves a Green-Schwarz mechanism mediated by RR partners of untwisted and/or twisted moduli. This class of models is of potential phenomenological interest, and we construct explicit examples of SU(3) x SU(2) x U(1) three-generation models. The models are non-supersymmetric, but the string scale may be lowered close to the weak scale so that the standard hierarchy problem is avoided. We also comment on the presence of scalar tachyons and possible ways to avoid the associated instabilities. We discuss the existence of (meta)stable configurations of D-branes on 3-cycles in (T^2)^3, free of tachyons for certain ranges of the six-torus moduli., Comment: 35 pages, latex. Minor mistakes in mass formulae corrected

We discuss both the UV and IR origin of the one-loop triangle gauge anomalies for noncommutative nonabelian chiral gauge theories with fundamental, adjoint and bi-fundamental fermions for U(N) groups. We find that gauge anomalies only come from planar triangle diagrams, the non-planar triangle contributions giving rise to no breaking of the Ward identies. Generally speaking, theories with fundamental and bi-fundamental chiral matter are anomalous. Theories with only adjoint chiral fermions are anomaly free., Comment: PlainTex, 21 pages, 2 eps figures, corrected some typos

In [Carey, A.L., J. Mickelsson, and M. K. Murray: Comm. Math. Phys. 183, 707 (1997)] Schwinger terms in hamiltonian quantization of chiral fermions coupled to vector potentials were computed, using some ideas from the theory of gerbes, with the help of the family index theorem for a manifold with boundary. Here, we generalize this method to include gravitational Schwinger terms., Comment: 23 pages

A recently proposed method for regularizing chiral gauge theories non-perturbatively is discussed in detail. The result is an effective action which can be computed from the lattice gauge field, and which is suited for numerical simulations., Talk given by G. Schierholz at Yukawa International Seminar on Non-Perturbative QCD: Structure of the QCD Vacuum (YKIS97), Kyoto, December 1997; typos corrected

The presence of chiral fermions in the physical Hilbert space implies consistency conditions on the spectral action. These conditions are equivalent to the absence of gauge and gravitational anomalies. Suggestions for the fermionic part of the spectral action are made based on the supersymmetrisation of the bosonic part., Comment: 10 pages, Latex file

In this note we derive the net number of generations of chiral fermions in heterotic string compactifications on Calabi-Yau threefolds with certain SU(n) vector bundles, for n odd, using the parabolic approach for bundles. We compare our results with the spectral cover construction for bundles and make a comment on the net number interpretation in F-theory., Comment: 8pp,latex,minor changes,note added

The anomaly due to the chiral fermions on the world-volume of the SO(32) five-brane is calculated. It is shown that this contribution has the correct structure for it to be cancelled by the variation of the classical world-volume action. The cancellation mechanism requires a Green-Schwarz-like term in the classical action. The result confirms the field content of the SO(32) five-brane proposed by Witten., 10 pages, LaTeX

We consider open supermembranes in eleven dimensions in the presence of closed M-Theory five-branes. It has been shown that, in a flat space-time, the world-volume action is kappa invariant and preserves a fraction of the eleven dimensional supersymmetries if the boundaries of the membranes lie on the five-branes. We calculate the reparametrisation anomalies due to the chiral fermions on the boundaries of the membrane and examine their cancellation mechanism. We show that these anomalies cancel with the aid of a classical term in the world-volume action, provided that the tensions of the five-brane and the membrane are related to the eleven dimensional gravitational constant in a way already noticed in M-Theory., Comment: Latex, 14 pages