All of the work presented in this thesis evolved from the initial idea that strings, if they are to make sense, ought to exist in four spacetime dimensions. At the time that it was formulated, back in mid-1985, such an idea was thought to be impossible. There were only five string theories that were known to be fully consistent, and each of these had a critical dimension of 10. The bosonic (or Veneziano) string has to live in 26 spacetime dimensions, or else a breakdown of Lorentz invariance occurs. But it is not a fully consistent theory because it contains a tachyon (a particle with negative mass squared) in its spectrum and its amplitudes have infinities. The open (type I) as well as the closed (type II) superstrings introduce supersymmetry into the theory, and this reduces the critical dimension from 26 down to 10. The type I superstring is N=1 supersymmetric, whereas the type II string is N=2. The E8 x E8 and Spin(32)/Z2 heterotic strings are hybrids (or heteroses) of the 10-dimensional superstring and compactified versions of the 26-dimensional bosonic string, and they too have ten as their critical number of dimensions. All of these theories have very appealing features in their critical number of dimensions, and the hope was to maintain as many of these features as possible while reducing the spacetime dimension down to what we know it must be on the everyday scale of events - namely four.
","abstract_html":"<p>All of the work presented in this thesis evolved from the initial idea that strings, if they are to make sense, ought to exist in four spacetime dimensions. At the time that it was formulated, back in mid-1985, such an idea was thought to be impossible. There were only five string theories that were known to be fully consistent, and each of these had a critical dimension of 10. The bosonic (or Veneziano) string has to live in 26 spacetime dimensions, or else a breakdown of Lorentz invariance occurs. But it is not a fully consistent theory because it contains a tachyon (a particle with negative mass squared) in its spectrum and its amplitudes have infinities. The open (type I) as well as the closed (type II) superstrings introduce supersymmetry into the theory, and this reduces the critical dimension from 26 down to 10. The type I superstring is N=1 supersymmetric, whereas the type II string is N=2. The E<sub>8</sub> x E<sub>8</sub> and Spin(32)/Z<sub>2</sub> heterotic strings are hybrids (or heteroses) of the 10-dimensional superstring and compactified versions of the 26-dimensional bosonic string, and they too have ten as their critical number of dimensions. All of these theories have very appealing features in their critical number of dimensions, and the hope was to maintain as many of these features as possible while reducing the spacetime dimension down to what we know it must be on the everyday scale of events - namely four. </p>","abstract_has_math":false,"creators":["Bluhm, Robert Theodore, Jr."],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Louise Dolan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1988,"date_issued":"1988-01-01T08:00:00Z","date_published":"1988-01-01T08:00:00Z","updated_at":"2026-07-24T04:10:47Z","subjects":["string theory","spacetime dimensions","critical dimensions","superstrings","bosonic string","supersymmetry","compactification","heterotic strings","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/486","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Louise Dolan"]},{"key":"dc:creator","label":"Author","values":["Bluhm, Robert Theodore, Jr."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["string theory","spacetime dimensions","critical dimensions","superstrings","bosonic string","supersymmetry","compactification","heterotic strings","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/486"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["All of the work presented in this thesis evolved from the initial idea that strings, if they are to make sense, ought to exist in four spacetime dimensions. At the time that it was formulated, back in mid-1985, such an idea was thought to be impossible. There were only five string theories that were known to be fully consistent, and each of these had a critical dimension of 10. The bosonic (or Veneziano) string has to live in 26 spacetime dimensions, or else a breakdown of Lorentz invariance occurs. But it is not a fully consistent theory because it contains a tachyon (a particle with negative mass squared) in its spectrum and its amplitudes have infinities. The open (type I) as well as the closed (type II) superstrings introduce supersymmetry into the theory, and this reduces the critical dimension from 26 down to 10. The type I superstring is N=1 supersymmetric, whereas the type II string is N=2. The E8 x E8 and Spin(32)/Z2 heterotic strings are hybrids (or heteroses) of the 10-dimensional superstring and compactified versions of the 26-dimensional bosonic string, and they too have ten as their critical number of dimensions. All of these theories have very appealing features in their critical number of dimensions, and the hope was to maintain as many of these features as possible while reducing the spacetime dimension down to what we know it must be on the everyday scale of events - namely four.
"]},{"key":"dc:title","label":"Title","values":["Superstrings in Four Dimensions"]}]}],"canonical_facts":{"dc:contributor":["Louise Dolan"],"dc:creator":["Bluhm, Robert Theodore, Jr."],"dc:description.abstract":["All of the work presented in this thesis evolved from the initial idea that strings, if they are to make sense, ought to exist in four spacetime dimensions. At the time that it was formulated, back in mid-1985, such an idea was thought to be impossible. There were only five string theories that were known to be fully consistent, and each of these had a critical dimension of 10. The bosonic (or Veneziano) string has to live in 26 spacetime dimensions, or else a breakdown of Lorentz invariance occurs. But it is not a fully consistent theory because it contains a tachyon (a particle with negative mass squared) in its spectrum and its amplitudes have infinities. The open (type I) as well as the closed (type II) superstrings introduce supersymmetry into the theory, and this reduces the critical dimension from 26 down to 10. The type I superstring is N=1 supersymmetric, whereas the type II string is N=2. The E8 x E8 and Spin(32)/Z2 heterotic strings are hybrids (or heteroses) of the 10-dimensional superstring and compactified versions of the 26-dimensional bosonic string, and they too have ten as their critical number of dimensions. All of these theories have very appealing features in their critical number of dimensions, and the hope was to maintain as many of these features as possible while reducing the spacetime dimension down to what we know it must be on the everyday scale of events - namely four.
"],"dc:identifier":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/486"],"dc:subject":["string theory","spacetime dimensions","critical dimensions","superstrings","bosonic string","supersymmetry","compactification","heterotic strings","Physical Sciences and Mathematics"],"dc:title":["Superstrings in Four Dimensions"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:10:47Z"}