The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex

Some components of the graviton two-point function have been recently computed in the context of loop quantum gravity, using the spinfoam Barrett-Crane vertex. We complete the calculation of the remaining components. We find that, under our assumptions, the Barrett-Crane vertex does not yield the correct long distance limit. We argue that the problem is general and can be traced to the intertwiner-independence of the Barrett-Crane vertex, and therefore to the well-known mismatch between the Barrett-Crane formalism and the standard canonical spin networks. In a companion paper we illustrate the asymptotic behavior of a vertex amplitude that can correct this difficulty.Comment: 31 page

Winthrop University Undergraduate Scholarship 2016 Book of Abstracts

University College and Winthrop University proudly present Undergraduate Scholarship and Creative Activity 2016. This is the fifth annual university-wide compilation of undergraduate work, christened with a new title that is more representative of the full range of students’ scholarly and creative efforts. This year’s book chronicles the accomplishments of students and faculty mentors from 25 academic departments and programs, spanning all five colleges of the university: College of Arts and Sciences (CAS), College of Business Administration (CBA), College of Education (COE), College of Visual and Performing Arts (CVPA), and University College (UC).https://digitalcommons.winthrop.edu/undergradresearch_abstractbooks/1013/thumbnail.jp

Fivebranes and 4-manifolds

We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which include new 3d N=2 theories T[M_3] associated with rational homology spheres and new results for Vafa-Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0,2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines / walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N=(0,2) theories and 3d N=2 theories, respectivelyComment: 81 pages, 18 figures. v2: misprints corrected, clarifications and references added. v3: additions and corrections about lens space theory, 4-manifold gluing, smooth structure