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[3] viXra:2607.0030 [pdf] submitted on 2026-07-08 08:34:27
Authors: Sutirtha Mukherjee
Comments: 292 Pages.
Perturbative string theory treats a moving string as a two-dimensional surface and studies the quantum field theory of the fields living on it. Removing the two gauge freedoms of that surface, the freedom to relabel its points and the freedom to rescale its metric, by the Faddeev--Popov method produces a nilpotent BRST charge $Q_B$, and its cohomology $H(Q_B)$ is the physical spectrum of the string. The condition $Q_B^2=0$ fixes the number of spacetime dimensions at twenty-six for the bosonic string and ten for the superstring. At one loop the surface is a torus, and its modular invariance chooses the allowed spectrum, the GSO projection of the superstring, and the charge lattices the theory can carry. The same degeneration limit gives unitarity, since the amplitude factorizes on physical intermediate states. When that intermediate state is a massless one emitted into the vacuum, its coefficient is a tadpole, and requiring the tadpole to vanish is what picks out an allowed background. For the unoriented open string, this condition, equivalently the cancellation of gauge anomalies, forces the gauge group $SO(32)$. These results, and the tree and loop amplitudes built from them, make up the perturbative theory. Perturbation theory is limited to weak coupling, and reaching strong coupling relies on a set of non-perturbative probes that supersymmetry protects. A single cylinder stretched between two D-branes can be understood in two ways, as a loop of open string and as a closed string exchanged across the gap, and equating the two fixes the tension of a D-brane and shows that its Ramond-Ramond charge is quantized in the smallest unit Dirac allows. The masses of the bound states the branes form, the $(p,q)$ strings, and the D0-brane threshold bound states are set exactly by the supersymmetry algebra. Because these tensions, charges, and masses do not move with the coupling, they can be compared across two descriptions of the physics. The $(p,q)$ strings fill out the $SL(2,mathbb Z)$ multiplet behind the S-duality of type~IIB, and the D0-branes become the momentum modes of an eleventh dimension that opens up in strongly coupled type~IIA. The same protected states count the microstates of a black hole and reproduce its Bekenstein-Hawking entropy, and D-branes sourcing a warped throat give a four-dimensional gauge theory that confines while keeping one massless particle.
Category: Quantum Gravity and String Theory
[2] viXra:2607.0012 [pdf] submitted on 2026-07-06 19:54:39
Authors: Sutirtha Mukherjee
Comments: 104 Pages. (Note by viXra Admin: Please cite listed scientific references)
This work presents a systematic development of conformal field theory from first principles in quantum field theory, emphasizing complete derivations of the conformal group in arbitrary dimensions from the conformal Killing equation, proving its isomorphism to $mathrm{SO}(d+1,1)$, and develop the embedding space formalism as a tool for constructing conformally covariant correlation functions constrained by Ward identities. In two dimensions, conformal symmetry enhances to an infinite-dimensional algebra: we derive the Virasoro algebra $[L_m, L_n] = (m-n)L_{m+n} + frac{c}{12}(m^3-m)delta_{m+n,0}$ from infinitesimal generators $ell_n = -z^{n+1}partial_z$, computing the central charge explicitly for free theories (boson $c=1$, Majorana fermion $c=1/2$, $bc$-ghosts $c = 1-3(2lambda-1)^2$) and demonstrating its physical interpretation as vacuum energy. Through radial quantization, we establish the operator-state correspondence and construct the Hilbert space via Virasoro descendants of primary states $|h,bar{h}angle$, deriving the transformation law $T'(w) = (dw/dz)^{-2}[T(z) - (c/12){w;z}]$ that reveals the geometric origin of the conformal anomaly. Unlike conventional treatments, we develop all mathematical machinery from standard QFT without relying on unexplained results from string theory or representation theory, exhibiting all intermediate steps explicitly to provide a detailed continuation beyond introductory QFT texts.
Category: Quantum Gravity and String Theory
[1] viXra:2607.0003 [pdf] submitted on 2026-07-01 08:20:09
Authors: Holger Döring
Comments: 26 Pages.
In a former paper a quantum induced warp-drive was introduced by assuming a model of microscopic cylinders as spacelike dimensions whereby the timelike dimension remains at its classical one-dimensional state. Described now is more detailed the underlying fundamental physical and mathematical spacetime structure than in the first paper , which is announced to feature this quantum induced warp-drive concept. Although there are certainly some new elements involved, everything is based on very classical GRT and QTH- descriptions. A more detailed description of the coupling dilaton-field is made, which connects the macroscopic sector of GRT with the microscopic sector of QFTH. This dilaton-field shall be named a "barytic -field".
Category: Quantum Gravity and String Theory
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