scholarly journals ANOMALIES OF E8 GAUGE THEORY ON STRING MANIFOLDS

2011 ◽  
Vol 26 (13) ◽  
pp. 2177-2197 ◽  
Author(s):  
HISHAM SATI
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Spin Structure ◽  
Heterotic String Theory ◽  
String Structure ◽  
The Subject ◽  
Global Anomaly ◽  
The One ◽  
M Theory ◽  
Witten Genus

In this paper we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with string structure and give three observations. First, that on string manifolds there is no E8 × E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory partition function of Diaconescu–Moore–Witten extends from the spin case to the string case. Third, that the cubic refinement law of Diaconescu–Freed–Moore for the phase of the M-theory partition function extends to string manifolds. The analysis relies on extending from invariants which depend on the spin structure to invariants which instead depend on the string structure. Along the way, the one-loop term is refined via the Witten genus.

FIVEBRANE STRUCTURES

2009 ◽  
Vol 21 (10) ◽  
pp. 1197-1240 ◽  
Author(s):  
HISHAM SATI ◽  
URS SCHREIBER ◽  
JIM STASHEFF
Keyword(s):  
String Theory ◽  
Heterotic String ◽  
Target Space ◽  
Type Ii ◽  
Anomaly Cancellation ◽  
Heterotic String Theory ◽  
Dual Version ◽  
String Structure ◽  
Topological Obstructions ◽  
The One

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

THE ANOMALY CONSIDERATION OF O(16) × O(16) HETEROTIC STRING THEORY

1987 ◽  
Vol 02 (07) ◽  
pp. 531-539 ◽  
Author(s):  
YOUNG HUN KWON
Keyword(s):  
String Theory ◽  
Low Energy ◽  
Heterotic String ◽  
Energy Limit ◽  
Heterotic String Theory ◽  
Energy Theory ◽  
Global Anomaly

To a tachyon-free O (16) × O (16) heterotic string theory with anomaly-free properties in the low energy limit, we consider the anomaly of the compactified theory in 8, 6 and 4 dimensions. Furthermore, we investigate the global anomaly of the theory and discuss the compactified manifold which will give a consistent low energy theory.

scholarly journals “Lagrangian disks” in M-theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Sebastían Franco ◽  
Sergei Gukov ◽  
Sangmin Lee ◽  
Rak-Kyeong Seong ◽  
James Sparks
Keyword(s):  
String Theory ◽  
Large Class ◽  
Lagrangian Submanifolds ◽  
The Other ◽  
Holomorphic Curves ◽  
Special Lagrangian ◽  
Special Lagrangian Submanifolds ◽  
Brane Models ◽  
The One ◽  
M Theory

Abstract While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M4] on the other.

scholarly journals ON EFFECTIVE F-THEORY ACTION IN TYPE IIA COMPACTIFICATIONS

2007 ◽  
Vol 22 (07) ◽  
pp. 1279-1300 ◽  
Author(s):  
IGOR KRIZ ◽  
HAO XING
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Effective Action ◽  
Space Time ◽  
Elliptic Cohomology ◽  
Pontrjagin Class ◽  
Geometric Term ◽  
M Theory ◽  
Special Case

Diaconescu, Moore and Witten proved that the partition function of type IIA string theory coincides (to the extent checked) with the partition function of M-theory. One of us (Kriz) and Sati proposed in a previous paper a refinement of the IIA partition function using elliptic cohomology and conjectured that it coincides with a partition function coming from F-theory. In this paper, we define the geometric term of the F-theoretical effective action on type IIA compactifications. In the special case when the first Pontrjagin class of space–time vanishes, we also prove a version of the Kriz–Sati conjecture by extending the arguments of Diaconescu–Moore–Witten. We also briefly discuss why even this special case allows interesting examples.

scholarly journals The topological line of ABJ(M) theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nicola Gorini ◽  
Luca Griguolo ◽  
Luigi Guerrini ◽  
Silvia Penati ◽  
Domenico Seminara ◽  
...  
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Exact Representation ◽  
One Dimensional ◽  
Topological Sector ◽  
The Matrix ◽  
The One ◽  
The Masses ◽  
Dimension One ◽  
M Theory

Abstract We construct the one-dimensional topological sector of $$ \mathcal{N} $$ N = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

SUPERCONFORMAL SYMMETRY AND GEOMETRY OF RICCI-FLAT KÄHLER MANIFOLDS

1989 ◽  
Vol 04 (17) ◽  
pp. 4303-4324 ◽  
Author(s):  
HIROSI OOGURI
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Superconformal Algebra ◽  
Heterotic String ◽  
Modular Invariant ◽  
Heterotic String Theory ◽  
Superconformal Symmetry ◽  
Ricci Flat ◽  
Particle Spectra ◽  
Compactified Space

A supersymmetric nonlinear σ-model provides us a tool for studying the dynamics of superstrings on a compactified space. If the compactified space is a Ricci-flat Kähler manifold, the nonlinear σ-model has extended superconformal symmetry and the partition function of the model is expressed in terms of characters of the superconformal algebra. The partition function must be modular invariant and this condition gives strong constraints on the spectrum of the model. These constraints are intimately related to geometry of the compactified space. Their implications to particle spectra of the compactified heterotic string theory are also discussed.

scholarly journals GEOMETRY OF SPIN ANDSPINcSTRUCTURES IN THE M-THEORY PARTITION FUNCTION

2012 ◽  
Vol 24 (03) ◽  
pp. 1250005 ◽  
Author(s):  
HISHAM SATI
Keyword(s):  
Partition Function ◽  
Fundamental Group ◽  
Spin Structure ◽  
Index Theorem ◽  
Quantization Condition ◽  
Deligne Cohomology ◽  
Infinite Dimensional ◽  
Eta Invariants ◽  
K Theory ◽  
M Theory

We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta invariants upon variation of the Spin structure. The main sources of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spinccase and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in 10 dimensions, the (mod 2) index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the α-invariant, which in general depends on the Spin structure. This reveals many interesting connections to positive scalar curvature manifolds and constructions related to the Gromov–Lawson–Rosenberg conjecture. In the 12-dimensional theory bounding M-theory, we study similar geometric questions, including choices of metrics and obtaining elements of K-theory in 10 dimensions by pushforward in K-theory on the disk fiber. We interpret the latter in terms of the families index theorem for Dirac operators on the M-theory circle and disk. This involves superconnections, eta forms, and infinite-dimensional bundles, and gives elements in Deligne cohomology in lower dimensions. We illustrate our discussion with many examples throughout.

“Channeling” the powers of God’s Word

2010 ◽  
Vol 4 (2) ◽  
pp. 135-156 ◽  
Author(s):  
Dorothea E. Schulz
Keyword(s):  
The Other ◽  
Border Zone ◽  
Focus Attention ◽  
Spiritual Power ◽  
New Materials ◽  
God's Word ◽  
Audio Recordings ◽  
Heated Debate ◽  
The Subject ◽  
The One

Starting with the controversial esoteric employment of audio recordings by followers of the charismatic Muslim preacher Sharif Haidara in Mali, the article explores the dynamics emerging at the interface of different technologies and techniques employed by those engaging the realm of the Divine. I focus attention on the “border zone” between, on the one hand, techniques for appropriating scriptures based on long-standing religious conventions, and, on the other, audio recording technologies, whose adoption not yet established authoritative and standardized forms of practice, thereby generating insecurities and becoming the subject of heated debate. I argue that “recyclage” aptly describes the dynamics of this “border zone” because it captures the ways conventional techniques of accessing the Divine are reassessed and reemployed, by integrating new materials and rituals. Historically, appropriations of the Qur’an for esoteric purposes have been widespread in Muslim West Africa. These esoteric appropriations are at the basis of the considerable continuities, overlaps and crossovers, between scripture-related esoteric practices on one side, and the treatment by Sharif Haidara’s followers of audio taped sermons as vessels of his spiritual power, on the other.

PHILOSOPHICAL PROPAEDEUTICS IN THE SYSTEM OF PRESCHOOL EDUCATION

2020 ◽  
Vol 22 (11) ◽  
pp. 11-15
Author(s):  
Gan N.Yu. ◽  
Ponomareva L.I. ◽  
Obukhova K.A.
Keyword(s):  
Modern Science ◽  
Preschool Education ◽  
Modern Society ◽  
Social Relevance ◽  
The Social ◽  
Moral Problems ◽  
The Subject ◽  
The One ◽  
The Individual ◽  
And Training

Today, worldview, spiritual and moral problems that have always been reflected in education and upbringing come to the fore in society. In this situation, there is a demand for philosophical categories. One of the priority goals of education in modern conditions is the formation of a reasonable, reflexive person who is able to analyze their actions and the actions of other people. Modern science is characterized by an understanding of the absolute value and significance of childhood in the development of the individual, which implies the need for its multilateral study. In the conditions of democratization of all spheres of life, the child ceases to be a passive object of education and training, and becomes an active carrier of their own meanings of being and the subject of world creation. One of the realities of childhood is philosophizing, so it is extremely timely to address the identification of its place and role in the world of childhood. Children's philosophizing is extremely poorly studied, although the need for its analysis is becoming more obvious. Children's philosophizing is one of the forms of philosophical reflection, which has its own qualitative specificity, on the one hand, and commonality with all other forms of philosophizing, on the other. The social relevance of the proposed research lies in the fact that children's philosophizing can be considered as an intellectual indicator of a child's socialization, since the process of reflection involves the adoption and development of culture. Modern society, in contrast to the traditional one, is ready to "accept" a philosophizing child, which means that it is necessary to determine the main characteristics and conditions of children's philosophizing.

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