Yang-Hui He

D-brane gauge theories from toric singularities and toric duality

A self-contained electric power driven bolt actuator unit for installation with a high security door locking mechanism comprising a housing adapted to be mounted on the door in operative association with the lock mechanism, a rotatable actuator shaft being mounted in the housing and connected at one end with a bolt actuating cam, an electric motor connected to drive the actuator shaft through a friction driving connection, a manually operable knob for overriding the actuation of the bolt by the cam independently of the motor, and switching means operable upon predetermined rotation of the actuator shaft in each direction of its rotation to reverse the driving direction of said electric motor and for indicating the operative position of the bolt of the locking mechanism.

The Exact MSSM spectrum from string theory

We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line. Specifically, the observable sector is N=1 supersymmetric with gauge group SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons, each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair. Importantly, there are no extra vector-like pairs and no exotic matter in the zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge instanton moduli in the observable sector. The holomorphic SU(4) vector bundle of the observable sector is slope-stable.

Counting gauge invariants: the plethystic program

We propose a programme for systematically counting the single and multi-trace gauge invariant operators of a gauge theory. Key to this is the plethystic function. We expound in detail the power of this plethystic programme for world-volume quiver gauge theories of D-branes probing Calabi-Yau singularities, an illustrative case to which the programme is not limited, though in which a full intimate web of relations between the geometry and the gauge theory manifests herself. We can also use generalisations of Hardy-Ramanujan to compute the entropy of gauge theories from the plethystic exponential. In due course, we also touch upon fascinating connections to Young Tableaux, Hilbert schemes and the MacMahon Conjecture.

Unhiggsing the del Pezzo

We develop an unhiggsing procedure for finding the D-brane probe world volume gauge theory for blowups of geometries whose gauge theory data are known. As specific applications we unhiggs the well-studied theories for the cone over the third del Pezzo surface. We arrive at what we call pseudo del Pezzos and these will constitute a first step toward the understanding of higher, non toric del Pezzos. Moreover, our methods and results give further support for toric duality as well as obtaining superpotentials from global symmetry considerations.

Exploring Positive Monad Bundles And A New Heterotic Standard Model

A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models contains 91 standard-like models which we describe in detail. A closer analysis of Wilson-line breaking for these models reveals that none of them gives rise to precisely the matter field content of the standard model. We conclude that the entire set of positive two-term monads on complete intersection Calabi-Yau manifolds is ruled out on phenomenological grounds. We also take a first step in analyzing the larger class of non-positive monads. In particular, we construct a supersymmetric heterotic standard model within this class. This model has the standard model gauge group and an additional U(1)B−L symmetry, precisely three families of quarks and leptons, one pair of Higgs doublets and no anti-families or exotics of any kind.

The Particle spectrum of heterotic compactifications

Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional theory. Generic points in vector bundle moduli space manifest an identical spectrum. However, it is shown that on subsets of moduli space of co-dimension one or higher, the spectrum can abruptly jump to many different values. Both analytic and numerical data illustrating this phenomenon are presented. This result opens the possibility of tunneling or phase transitions between different particle spectra in the same heterotic compactification. In the course of this discussion, a classification of SU(5) GUT theories within a specific context is presented.

Determinants of operative mortality in reoperative coronary artery bypass grafting

Previously suggested risk factors for operative mortality in reoperative coronary artery bypass grafting are contradictory. Therefore, we analyzed our data of 622 patients who underwent reoperative bypass grafting from January 1986 through June 1993. Among these patients, 258 had saphenous vein grafts alone and 364 had internal mammary artery grafting, including unilateral (342 patients) and bilateral (22 patients) mammary artery grafting with or without additional saphenous vein grafting. Overall operative mortality was 11.4% for reoperation compared with only 3.6% for primary bypass grafting during the same time frame. To determine risk factors for mortality and the influence of internal mammary artery grafting on the outcome, we analyzed 82 variables (31 preoperative, 17 intraoperative, and 34 postoperative) by univariate analysis. Significant variables or the variables having a trend (p < 0.2) to be associated with the mortality were included in stepwise multiple logistic regression analyses. Two regression analyses were separately performed. Regression 1 only included preoperative and intraoperative variables whereas regression 2 included postoperative variables as well. The logistic regressions demonstrate that preoperative variables (low ejection fraction [p = 0.0002], old age [p = 0.003], female gender [p = 0.011], and history of arrhythmia [p = 0.023]), intraoperative variables (emergency operation [p = 0.0001] and long perfusion time [p = 0.0001]), and postoperative variables (complications) are independently associated with higher mortality. Unlike previously described results, aortic crossclamp time, route of cardioplegia, use of internal mammary artery, number of grafts, and year of operation are not associated with operative mortality. The identification of these risk factors may have important implications in further improvement of the results of reoperative coronary artery bypass grafting.

Monad bundles in heterotic string compactifications

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 × E8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.

Non-abelian finite gauge theories

We study orbifolds of N = 4 U(n) super-Yang-Mills theory given by discrete subgroups of SU(2) and SU(3). We have reached many interesting observations that have graph-theoretic interpretations. For the subgroups of SU(2), we have shown how the matter content agrees with current quiver theories and have offered a possible explanation. In the case of SU(3) we have constructed a catalogue of candidates for finite (chiral) N = 1 theories, giving the gauge group and matter content. Finally, we conjecture a McKay-type correspondence for Gorenstein singularities in dimension 3 with modular invariants of WZW conformal models. This implies a connection between a class of finite N = 1 supersymmetric gauge theories in four dimensions and the classification of affine SU(3) modular invariant partition functions in two dimensions.

Aortic valve replacement: Determinants of operative mortality

Contradictory results have been reported regarding risk factors for aortic valve replacement (AVR). This study was designed to investigate determinants of operative mortality for AVR with emphasis on concomitant coronary artery bypass grafting (CABG) and old age. Between January 1986 and June 1992, 371 patients with a mean age of 61.99 +/- 0.76 years underwent AVR. There were 256 men (69.0%) and 115 women (31.0%). Twenty-six patients (7.0%) were 80 years old or older, and 97 (26.1%) were between 70 and 80 years old. Of these patients, 210 (56.6%) had isolated AVR, 142 (38.3%) had concomitant CABG, and 31 (8.4%) had concomitant mitral valve operations. Twenty patients (5.4%) underwent emergency operation. There were 33 operative deaths (8.9%). Univariate analysis and stepwise multiple logistic regression analysis were used to determine the risk factors for operative mortality. In the univariate analysis, 13 preoperative variables (sex, age, history of congestive heart failure, myocardial infarction, arrhythmia, functional class, class I/II versus III/IV, four variables related to aortic valve pathology, ejection fraction, left ventricular function) and 20 perioperative variables (emergency operation, individual surgeon, myocardial protection by type and route of cardioplegia, type of prosthesis, size of prosthesis, mean size by survival, small versus large size, concomitant procedure, concomitant CABG (versus others or AVR alone), concomitant mitral valve operation (versus others or AVR alone), concomitant CABG and MV operation, aortic cross-clamp time, cardiopulmonary bypass time, use and time of insertion of intraaortic balloon pump, low cardiac output, postoperative complications) were examined.(ABSTRACT TRUNCATED AT 250 WORDS)