511 research outputs found
3D gauged supergravity from SU(2) reduction of 6D supergravity
We obtain Yang-Mills gauged supergravity in three dimensions
from group manifold reduction of (1,0) six dimensional supergravity
coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in
the adjoint of . The reduced theory is consistently truncated to 3D
supergravity coupled to bosonic and fermionic propagating degrees of freedom. This is in contrast to the
reduction in which there are also massive vector fields. The scalar manifold is
, and there is a gauge group. We then
construct Chern-Simons three dimensional gauged supergravity with scalar
manifold and
explicitly show that this theory is on-shell equivalent to the Yang-Mills
gauged supergravity theory obtained from the reduction,
after integrating out the scalars and gauge fields corresponding to the
translational symmetries .Comment: 24 pages, no figures, references added and typos correcte
On Subleading Contributions to the AdS/CFT Trace Anomaly
In the context of the AdS/CFT correspondence, we perform a direct computation
in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find
agreement with the field theory result up to next to leading order in the 1/N
expansion. In particular, the order N gravitational contribution to the anomaly
is obtained from a Riemann tensor squared term in the 7-brane effective action
deduced from heterotic - type I duality. We also discuss, in the AdS/CFT
context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs
involving SO or Sp gauge groups.Comment: 25 pages, LaTeX, v2: references adde
Structure constants of planar N =4 Yang Mills at one loop
We study structure constants of gauge invariant operators in planar N=4
Yang-Mills at one loop with the motivation of determining features of the
string dual of weak coupling Yang-Mills. We derive a simple renormalization
group invariant formula characterizing the corrections to structure constants
of any primary operator in the planar limit. Applying this to the scalar SO(6)
sector we find that the one loop corrections to structure constants of gauge
invariant operators is determined by the one loop anomalous dimension
Hamiltonian in this sector. We then evaluate the one loop corrections to
structure constants for scalars with arbitrary number of derivatives in a given
holomorphic direction. We find that the corrections can be characterized by
suitable derivatives on the four point tree function of a massless scalar with
quartic coupling. We show that individual diagrams violating conformal
invariance can be combined together to restore it using a linear inhomogeneous
partial differential equation satisfied by this function.Comment: 52 pages, 12 figures, Typos fixed, reference adde
Towards a string bit formulation of N=4 super Yang-Mills
We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can
be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We
show that these oscillators can serve as world-sheet variables, the string
bits, of a discretized string. There is a one to one correspondence between the
on shell gauge invariant words of the free Y-M theory and the states in the
oscillators' Hilbert space, obeying a local gauge and cyclicity constraints.
The planar two-point functions and the three-point functions of all gauge
invariant words are obtained by the simple delta-function overlap of the
corresponding discrete string world sheet. At first order in the 't Hooft
coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of
the planar two-point and the three-point functions can be incorporated by
nearest neighbour interactions among the discretized string bits. In the SU(2)
sub-sector we show that the one-loop corrections to the structure constants can
be uniquely determined by the symmetries of the bit picture. For the SU(2)
sub-sector we construct a gauged, linear, discrete world-sheet model for the
oscillators, with only nearest neighbour couplings, which reproduces the
anomalous dimension Hamiltonian up to two loops. This model also obeys BMN
scaling to all loops.Comment: 64 pages, 6 figures, typos fixed, references adde
Dampak Kebijakan Lokal terhadap Efisiensi dan Efektivitas Penatausahaan Keuangan Daerah pada Pemerintahan Kabupaten Ketapang
This research writing have aim to know and analyse the excess and lack of local policy for orderer of Financially in this time executed in Regency of Ketapang and also to analyse the local policy execution impact to efficiency and effectiveness Financially Region at Commanding Regency of Ketapang. Data Type used is data qualitative from Government of Ketapang Regency, steming from direct interconnected informano by orderer of finance in Regency of Ketapang and also other source consisted by the letter, law and regulation, book, and bound up official documents. Result of Research that local policy in Regency of Ketapang most is not effective and inefficient, but that way domestic minister policy also there are some which is not effective Keywords : Local Policy, Efficiency, Effectiveness, Area Financ
Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes
We present a class of 3D Black Holes based on flat connections which are
polynomials in the BTZ -valued connection. We
solve analytically the fluctuation equations of matter in their background and
find the spectrum of their Quasi Normal Modes. We analyze the bulk to boundary
two-point functions. We also relate our results and those arising in other
backgrounds discussed recently in the literature on the subject.Comment: v3: typo corrected in first line of Eq (4.2), improved presentatio
Exploring the future of mathematics teaching: Insight with ChatGPT
This study aims to provide a comprehensive overview of the future of mathematics teaching from the perspective of ChatGPT, an advanced language processing artificial intelligence (AI) developed by OpenAI. The results of the chat transcripts edited with ChatGPT suggest that the future of mathematics teaching will see the integration of technology and AI to provide personalized learning experiences, blended learning environments, and computational thinking, data literacy, and statistics. Problem-solving, critical thinking, and interdisciplinary connections will continue to be emphasized, and equity and inclusion will remain crucial. AI is expected to revolutionize mathematics education, but thoughtful implementation, ongoing professional development, and pedagogical considerations are essential. However, the future of teaching mathematics will continue to evolve. Therefore, teachers and lecturers need to keep abreast of the latest developments and adapt to them while remaining committed to providing quality teaching.Studi ini bertujuan untuk memberikan gambaran komprehensif tentang masa depan pengajaran matematika dari perspektif ChatGPT, Artificial Intelligence (AI) pemrosesan bahasa tingkat lanjut yang dikembangkan oleh OpenAI. Hasil transkrip obrolan yang diedit dengan ChatGPT menunjukkan bahwa masa depan pengajaran matematika akan melihat integrasi teknologi dan AI untuk memberikan pengalaman belajar yang dipersonalisasi, lingkungan pembelajaran campuran, dan pemikiran komputasi, literasi data, dan statistik. Pemecahan masalah, pemikiran kritis, dan koneksi interdisipliner akan terus ditekankan, dan kesetaraan dan inklusi akan tetap penting. AI diharapkan merevolusi pendidikan matematika, tetapi implementasi yang bijaksana, pengembangan profesional berkelanjutan, dan pertimbangan pedagogis sangat penting. Namun, masa depan pengajaran matematika akan terus berkembang. Oleh karena itu, guru dan dosen perlu mengikuti perkembangan terkini dan beradaptasi dengannya sambil tetap berkomitmen untuk memberikan pengajaran yang berkualitas
- …