Cluster decomposition, T-duality, and gerby CFT's

In this paper we study CFT's associated to gerbes. These theories suffer from a lack of cluster decomposition, but this problem can be resolved: the CFT's are the same as CFT's for disconnected targets. Such theories also lack cluster decomposition, but in that form, the lack is manifestly not very problematic. In particular, we shall see that this matching of CFT's, this duality between noneffective gaugings and sigma models on disconnected targets, is a worldsheet duality related to T-duality. We perform a wide variety of tests of this claim, ranging from checking partition functions at arbitrary genus to D-branes to mirror symmetry. We also discuss a number of applications of these results, including predictions for quantum cohomology and Gromov-Witten theory and additional physical understanding of the geometric Langlands program.Comment: 61 pages, LaTeX; v2,3: typos fixed; v4: writing improved in several sections; v5: typos fixe

Non-birational twisted derived equivalences in abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kahler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kahler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov's `homological projective duality.' Along the way, we shall see how `noncommutative spaces' (in Kontsevich's sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.Comment: 54 pages, LaTeX; v2: typo fixe

Rigidly Supersymmetric Gauge Theories on Curved Superspace

In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein four-manifolds such as AdS$_4$, N=1 rigidly supersymmetric sigma models are constrained to have target spaces with exact K\"ahler forms. Similarly, in gauged sigma models and gauge theories, we find that supersymmetry imposes constraints on Fayet-Iliopoulos parameters, which have the effect of enforcing that K\"ahler forms on quotient spaces be exact. We also discuss general aspects of universality classes of gauged sigma models, as encoded by stacks, and also discuss affine bundle structures implicit in these constructions.Comment: 23 pages; references added; more discussion added; v4: typos fixe

The Γ^\hat{\Gamma}-genus and a regularization of an S1S^1-equivariant Euler class

We show that a new multiplicative genus, in the sense of Hirzebruch, can be obtained by generalizing a calculation due to Atiyah and Witten. We introduce this as the $\hat{\Gamma}$-genus, compute its value for some examples and highlight some of its interesting properties. We also indicate a connection with the study of multiple zeta values, which gives an algebraic interpretation for our proposed regularization procedure.Comment: 14 pages; version to appear in J. Phys.

Playing and Listening to Tailor-Made Notched Music: Cortical Plasticity Induced by Unimodal and Multimodal Training in Tinnitus Patients

Background. The generation and maintenance of tinnitus are assumed to be based on maladaptive functional cortical reorganization. Listening to modified music, which contains no energy in the range of the individual tinnitus frequency, can inhibit the corresponding neuronal activity in the auditory cortex. Music making has been shown to be a powerful stimulator for brain plasticity, inducing changes in multiple sensory systems. Using magnetoencephalographic (MEG) and behavioral measurements we evaluated the cortical plasticity effects of two months of (a) active listening to (unisensory) versus (b) learning to play (multisensory) tailor-made notched music in nonmusician tinnitus patients. Taking into account the fact that uni- and multisensory trainings induce different patterns of cortical plasticity we hypothesized that these two protocols will have different affects. Results. Only the active listening (unisensory) group showed significant reduction of tinnitus related activity of the middle temporal cortex and an increase in the activity of a tinnitus-coping related posterior parietal area. Conclusions. These findings indicate that active listening to tailor-made notched music induces greater neuroplastic changes in the maladaptively reorganized cortical network of tinnitus patients while additional integration of other sensory modalities during training reduces these neuroplastic effects

F-theory, Geometric Engineering and N=1 Dualities

We consider geometric engineering of N=1 supersymmetric QFTs with matter in terms of a local model for compactification of F-theory on Calabi-Yau fourfold. By bringing 3-branes near 7-branes we engineer N=1 supersymmetric $SU(N_c)$ gauge theory with $N_f$ flavors in the fundamental. We identify the Higgs branch of this system with the instanton moduli space on the compact four dimensional space of the 7-brane worldvolume. Moreover we show that the Euclidean 3-branes wrapped around the compact part of the 7-brane worldvolume can generate superpotential for $N_f=N_c-1$ as well as lead to quantum corrections to the moduli space for $N_f=N_c$. Finally we argue that Seiberg's duality for N=1 supersymmetric QCD may be mapped to T-duality exchanging 7-branes with 3-branes.Comment: 15 page

Enhancing Inhibition-Induced Plasticity in Tinnitus – Spectral Energy Contrasts in Tailor-Made Notched Music Matter

Chronic tinnitus seems to be caused by reduced inhibition among frequency selective neurons in the auditory cortex. One possibility to reduce tinnitus perception is to induce inhibition onto over-activated neurons representing the tinnitus frequency via tailor-made notched music (TMNM). Since lateral inhibition is modifiable by spectral energy contrasts, the question arises if the effects of inhibition-induced plasticity can be enhanced by introducing increased spectral energy contrasts (ISEC) in TMNM. Eighteen participants suffering from chronic tonal tinnitus, pseudo randomly assigned to either a classical TMNM or an ISEC-TMNM group, listened to notched music for three hours on three consecutive days. The music was filtered for both groups by introducing a notch filter centered at the individual tinnitus frequency. For the ISEC-TMNM group a frequency bandwidth of 3/8 octaves on each side of the notch was amplified, additionally, by about 20 dB. Before and after each music exposure, participants rated their subjectively perceived tinnitus loudness on a visual analog scale. During the magnetoencephalographic recordings, participants were stimulated with either a reference tone of 500 Hz or a test tone with a carrier frequency representing the individual tinnitus pitch. Perceived tinnitus loudness was significantly reduced after TMNM exposure, though TMNM type did not influence the loudness ratings. Tinnitus related neural activity in the N1m time window and in the so called tinnitus network comprising temporal, parietal and frontal regions was reduced after TMNM exposure. The ISEC-TMNM group revealed even enhanced inhibition-induced plasticity in a temporal and a frontal cortical area. Overall, inhibition of tinnitus related neural activity could be strengthened in people affected with tinnitus by increasing spectral energy contrast in TMNM, confirming the concepts of inhibition-induced plasticity via TMNM and spectral energy contrasts

Nonlinear Dynamics of the Perceived Pitch of Complex Sounds

We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility

Gamma and beta frequency oscillations in response to novel auditory stimuli: A comparison of human electroencephalogram (EEG) data with in vitro models

Investigations using hippocampal slices maintained in vitro have demonstrated that bursts of oscillatory field potentials in the gamma frequency range (30-80 Hz) are followed by a slower oscillation in the beta 1 range (12-20 Hz). In this study, we demonstrate that a comparable gamma-to-beta transition is seen in the human electroencephalogram (EEG) in response to novel auditory stimuli. Correlations between gamma and beta 1 activity revealed a high degree of interdependence of synchronized oscillations in these bands in the human EEG. Evoked (stimulus-locked) gamma oscillations preceded beta 1 oscillations in response to novel stimuli, suggesting that this may be analogous to the gamma-to-beta shift observed in vitro. Beta 1 oscillations were the earliest discriminatory responses to show enhancement to novel stimuli, preceding changes in the broad-band event-related potential (mismatch negativity). Later peaks of induced beta activity over the parietal cortex were always accompanied by an underlying gamma frequency oscillation as seen in vitro. A further analogy between in vitro and human recordings was that both gamma and beta oscillations habituated markedly after the initial novel stimulus presentation

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione